Problems Review

Explain why and how marginal analysis can be used to... 1) Max TR 2) Min TC in the short-run 3) Max total output in the short-run

1) where MR =0 2) where MC = 0 3) where MP =0

Economists assume that the primary goal of firms is to maximize profits. Explain how the firm achieves this goal. Illustrate with graphs

- Profits are TR - TC - Firms max their profits by producing an amount where MR = MC, provided that the TR curve is greater than the TC curve. - Q (controllable variable) should correspond to the level at which MNB = 0; nothing more can be gained by further changes in that variable

You have just opened a new grocery store. Every item you carry is generic. You recently read an article in the Wall Street Journal reporting that the price of recreation is expected to increase by 15%. How will it affect your store's sales of generic food products? Cross-price elasticity for food and transportation is 0.15.

0.15 = (%changeQxd)/(15) %changeQxd = 2.25 Thus, food and recreation are substitutes. If the price of recreation increases by 15%, you can expect the demand for generic good products to increase by 2.25%.

Identify five other important goals other than profit max?

1) Growth 2) Social and environmental 3) Maximizing ROI 4) Improving customer experience 5) Shareholder value

What are four other consequences of rent control, in addition to the shortage?

1) discrimination 2) waitlists 3) sublets 4) black market rents

The best estimates of the market demand and supply for the good are given by Qd = 10 - 2P a d Qs = 2 + 2P, respectively. Determine the equilibrium price and quantity.

Competitive equilibrium is determined by the intersection of the market demand and supply curves. Mathematically, this simply means that Qd = Qs. Thus equating demand and supply yields: 10 - 2P = 2 + 2P or 8 = 4P Solving this equation for P yields the equilibrium price which is $2. To determine the equilibrium quantity, plug in the price into the demand or supply curve which equates 6 units.

Qd = 20 - 2P, Qs = 5 + 3P Determine the total tax revenue earned by the government, the amount of the tax paid by consumers, and the amount of tax paid by sellers

Earned by the gov: T = P(tax) * Q T = 5*8 = $40 Paid by consumer: (Pnew - Pold) *Q (6-3)*8 = $24 Paid by the seller: 40-24 = $16

The demand for good X is given by this equation: Qx = 1.0 - 2.0Px + 0.8I + 1.5Py - 3Pz + 1.0A where Px, Py, and Pz represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. Currently: Px = 2, Py= 2.5, Pz=1, I=4 and A=3.05. Calculate the advertising elasticity of demand for X. Interpret your answer.

Eqx, a = 1 (3.05/4) = 0.7625 The advertising elasticity for good x is positive so advertisement has an inelastic demand. A 10% increase in advertising will increase demand by 7.625%.

The demand for good X is given by this equation: Qx = 1.0 - 2.0Px + 0.8I + 1.5Py - 3Pz + 1.0A where Px, Py, and Pz represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. Currently: Px = 2, Py= 2.5, Pz=1, I=4 and A=3.05. Calculate the cross elasticity of demand ofr C with respect to the price of good Z. Are goods X and Z substitutes or complements?

Eqx, py = -3/(1/4) =-0.75 Since x and z show a negative cross elasticity of demand, meaning that as the price of good Y rises, the demand for good x falls, this indicates that they are complements of each other.

Assume that managers take two years off without pay to complete an MBA. Use the concepts of opportunity cost and NPV to explain how you would measure if an MBA is profitable.

In order to measure whether an MBA is profitable, the NPV would need to be positive. The NPV of the MBA is the PV of the expected increase in salary and benefits less the PV of the cost of the MBA. The fees would include tuition, fees, textbooks and loss of wages. As explained above, to get an accurate NOV you need good and concrete estimates of both future income and benefits as well as appropriate discount rates in this case, the estimate is very risky.

The demand for good X is given by this equation: Qx = 1.0 - 2.0Px + 0.8I + 1.5Py - 3Pz + 1.0A where Px, Py, and Pz represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. Currently: Px = 2, Py= 2.5, Pz=1, I=4 and A=3.05. IS good X a necessity or a luxury good? How do you know?

Income elasticity Eqx = 0.8(4/4) = 0.8 The demand is income inelastic because it is greater than 1 therefore it is a necessary good.

The demand for Wanderlust Travel Services (X) is estimated to be: Qx = 22,000 - 2.5Px +4Py - M + 1.5Ax where Ax = advertising M = income per capita Suppose the price of good X is $450, good Y sells for $40, the company utilizes 3000 units of advertising, and consumer income is $20,000. Should the price of good X be raised to increase TR? Explain why or why not?

Increase price since demand is inelastic. As I have noted above, in this case, an increase in rice will increase the revenue because the change in price is lower than the change in quantity. For example, if price were to increase by 10% then quantity would reduce 2% which will increase TR because TR = P*Q.

Why is it important for economists to distinguish between demand and quantity demanded. Use graphs.

Market demand curve - identifies the different quantities of a good or service consumers are willing and able to buy at different prices, holding everything else constant. Change in demand - refers to a shift in the entire demand curve and thus consumers are willing and able to buy more at the same prices. Change in quantity demanded - refers to a movement along the demand curve. Quantity demanded is only affected by a change in PRICE. This is shown by a movement along the demand curve. Since price is measured explicitly on the y axis, it is the movement variable. Since there are only two axes, changes in other variables must shift the function. Change in demand refers to shifts in the entire demand curve caused by some change factor other than price. These factors may include: change in the number of buyers, change in income, change in price of related goods, substitutes and complements, change in tastes and preferences and changes in expected future prices or income changes.

The demand for Wanderlust Travel Services (X) is estimated to be: Qx = 22,000 - 2.5Px +4Py - M + 1.5Ax where Ax = advertising M = income per capita Suppose the price of good X is $450, good Y sells for $40, the company utilizes 3000 units of advertising, and consumer income is $20,000. Calculate consumer surplus at the profit maximizing price if the marginal cost is $264.

Need to find Qx = 6660 - 2.5Px Invert demand to get P = 2664 - 0.4Q and MR = 2664 - 0.8Q Set MR = MC 2664-0.8Q=264 Q= 3000 and P =1464 Consumer surplus is = 0.5(2664-1464)3000 = $1,800,000

The demand for good X is given by this equation: Qx = 1.0 - 2.0Px + 0.8I + 1.5Py - 3Pz + 1.0A where Px, Py, and Pz represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. Currently: Px = 2, Py= 2.5, Pz=1, I=4 and A=3.05. What kind of change in the price of X would you recommend if the firm is interested in maximizing revenue?

Own Price Elasticity Eqx,px = -2 (2.4) = -1 then |-1| = 1 The demand is unitary elastic thus TR has already been maximized. The price should NOT change.

Qd = 20 - 2P, Qs = 5 + 3P The government imposes a tax od $5. Find the new equilibrium price and quantity. Illustrate with the same graph from above.

Qd = Qs(with tax) 20 - 2P = 2 +3 (P -5) P = $6 Q = 20 - 2(6) = 8 units

The demand for Wanderlust Travel Services (X) is estimated to be: Qx = 22,000 - 2.5Px +4Py - M + 1.5Ax where Ax = advertising M = income per capita Suppose the price of good X is $450, good Y sells for $40, the company utilizes 3000 units of advertising, and consumer income is $20,000. Calculate the elasticity of demand for good X with respect to the price of X, the price of Y, income and advertising.

Qdx = 22,000 - 2.5(450) + 4(40) - 20,000 + 1.5(3,000) Qdx = 5,535 Ed = -2.5(450/5535) = -0.203 Cross-Price = (4)(40)/5535= -3.613 Advertising elasticity = 1.5 (3,000/5535) = 0.813 Since -0.203 <1, the demand is inelastic. An inelastic demand indicates that increases in price will increase the revenue because the change in price will be lower than the change in quantity.

Explain why rent control creates a shortage of rental housing. Illustrate with a supply/demand graph.

Rent control is a law placing a max price on what landlords may change tenants. The rent level must be set at a rate below market equilibrium price. At less than their equilibrium levels, the quantity demanded will exceed the quantity supplied, and rent control will lead to a shortage of space.

Your firm's research department has estimated the income elasticity of demand for nonfed ground beef to be -1.94. You just read that due to an upturn in the economy, consumer incomes are expected to rise by 10% over the next three years. As a manager of a meat-processing plant, how will this forecast affect your purchases of nonfed cattle?

Set Eqx,m = -1.94 and %changeM = 10 in the formula for the income elasticity of demand to obtain -1.94 = %changeQxd /10 = - 19.4 Since nonfed beef has an income elasticity of -1.94 and consumer income is expected to rise by 10 %, you can expect to sell 19.4% less nonfed ground beef over the next 3 years. Therefore, you should decrease your purchases of nonfed cattle by 19.4 %, unless something else changes.

Qd = 20 - 2P, Qs = 5 + 3P Determine the equilibrium price and quantity and illustrate with a graph.

Since equilibrium point is where Qd = Qs then, 20 - 2P = 5 + 3P P= 3 Qd = 20 - 2(3) = 14 Equating for P yields the equilibrium price of $3/unit. Then plugging this into the demand equation determines an equilibrium quantity of 14 units.

The manager of a fleet of cars currently rents them out at the market price of $49 per day, with renters paying for their own gasoline and oil. The managers learns that economists expect the prices to rise dramatically over the next year due to increased tensions in the Middle East. What should she expect to happen to the price of the cars her company rents?

Since gasoline and rental cars are complements, the increased in gas prices will decrease the demand for rental cars. To see this impact on the market price and quantity of rental cars, let D1 in Figure 2-13 represent the initial demand for rental cars, so that the initial equilibrium is at the point B. AN increase in the price of gasoline will shift the demand curve for rental cars to the left to D0 resulting in a new equilibrium at point A. Thus, she should expect the price of rental cars to fall.

What would happen if the chinese government privatized the market and then set a price ceiling at the Chinese equivalent of $1.50. How do you answer? Assume that the market demand and supply curves are still given by Qd = 10 - 2P a d Qs = 2 + 2P.

Since the price ceiling is below equilibrium price of $2, a shortage will result. More specifically, when the price ceiling is $1.50, quantity demanded is Qd = 10 - 2(1.5) = 7 and quantity supplied is Qs = 2 + 2(1.5) = 5 thus there is a shortage of 7 - 5 = 2 units. To determine the full economic price, we simply determine the maximum price consumers are willing to pay for the 5 units produced. To do this, we first set quantity equal to 5 in the demand formula: 5 = 10 - 2Pf or 2Pf = 5 Next, we solve for Pf to obtain the full economic price, Pf = $2.50; $1.50 of this price is in money and $1 represents the nonpecuniary price of the good. Lastly, we can solve for deadweight loss (Pf - Pc) (Qe - Qs) = (2.50 -1.50)(6-5) = 1.

What would happen if the Chinese government privatized the market but agreed to purchase (and discard) unsold units of the good at a floor price of $3.50. What would you tell the senator? Assume that the market demand and supply curves are still given by Qd = 10 - 2P a d Qs = 2 + 2P.

Since the price floor is above the equilibrium price of $2, the floor results in a surplus. More specifically, when price is $3.50, quantity demanded is Qd = 10 - 2(3.5) = 3 and quantity supplied is Qs = 2 + 2(3.5) = 9 Thus there is a surplus of 9 - 3 = 6 units. Consumers pay a higher price of $3.50, and producers have unsold inventories of 6 units. However, the Chinese government must purchase the amount consumers are unwilling to purchase at the price of $3.50. Therefore, the cost to the government is $3.50 * 6 = $21 The deadweight loss is compromised of the two shaded regions. The triangle has a deadweight of (3.5 - 0.5)(6 -3) = 9. The second part, the trapezoid is $21 - (1/2)(3.5 - 0.5)(6) = 12.

Explain fully the concept of NPV. Why and how can firms use NPV to determine which investments are most profitable? Provide a simple example.

The NPV of an investment is the PV of the expeted future revenues generated by the investment less the cost of the investment, The calculation requires both the estimate of future profits and appropriate discount rates (future interest rates). An investment is only profitable if NPV is positive and usually only projects with the highest NPV are undertaken. See example within these cards.

Qd = 20 - 2P, Qs = 5 + 3P What determines whether consumers or sellers pay the greater proportion of a tax such as the tax on cigarettes- in part a?

The elasticity of the supply and demand affect the tax incidence on consumers and producers. Whether consumers or sellers pay a greater proportion depends on the price elasticity of demand and supply for the product. Consumers pay more if demand is inelastic and supply is elastic. Sellers pay more if demand is elastic and supply is inelastic.

Explain fully the difference between economic and accounting profits. Provide one example of explicit cost and one example of an implicit cost. How do economists measure implicit costs?

The profit formulas the same where profits = TR - TC. The difference comes from how either considers TC. Accountants only consider explicit costs whereas economists consider both explicit and implicit costs. Explicit costs are easier to measure (costs of inputs). An example is the materials used in production. Implicit costs are the opportunity cost of using inputs owned by a firm. Opportunity cost is the explicit cost of a resource plus the implicit cost of giving up its best alternative use. An example is the additional costs that may go into training a new employee. The implicit cost is the labour the trainer has to take away from his current position to train.

Using marginal analysis, explain why the output which maximizes TR of a firm must exceed the output that maximizes total profits. Provide a single graph.

The total or average cost in comparison to the total or average benefit is often misleading which is why economists used marginal analysis to reach optimal decision making. Marginal analysis states that a decision will always be optimal as long as MB > MC. Marginal refers to additional rather than total. For example, in most cases a firm would want to charge a price that is greater than average costs. However, a plane with empty seats may want to chage a lower price as long as P > MC of that seat. MC cost in this case is much lower than av cost but the difference between price and MC will add to the total profits.

Idneity the winners and the losers in the rent control situation.

The winners are tenants who find rentals and the losers are landlords and renters who cannot find rentals due to the short supply.

The daily demand for Invigorated PED shoes is estimated to be: Qxd = 100 - 3 Px + 4Py - 0.01M + 2Ax Ax = amount of advertising spent on shoes (x) Px = the price of good X Py = price of good Y M = average income Suppose good X sells at $25 a pair, and good Y sells at $35, the company utilizes 50 units of advertising, and average consumer income is $20,000. Calculate and interpret the own price, cross-price, and income elasticities of demand.

To calculate the own price elasticity for linear demand, we use the formula: Eqxpx = ax*(Px/Qx) Here ax = -3 and px = 25. The only other information we need to calculate the elasticity is the quantity consumed of X. To find Qx, we substitute the given values of prices, income, and advertising into the demand function: Qxd= 100 - 3(25) + 4 (35) - 0.01 (20,000) + 2(50) = 65 units. Hence the own price elasticity of demand is given by Eqxpx = -3 (25/65) = -1.15 If Invigorated PED raised shoe prices, the percentage decline in the quantity demanded of its shoes will be greater in absolute value than the percentage rise in price. Consequently, demand is elastic: TR will fall if it raises shoe prices. Cross price elasticity of demand is: Eqx, py = 4 (35/65) = 2.15 Since this is positive, good Y is a subsitute for Invigorated PED shoes. The income elasticity of demand for Invigorated PED shoes is: Eq,m = -0.01 (20,000/65) = -3.08 Invigorated shoes are inferior goods since this is a negative number.

A manager is considering purchasing a new machine for $300,000 which is good for 5 years and has an interest rate of 8%. The machine would bring cost reductions of $50k (year 1), $60k (year 2), $75k (year 3), $90k (year 4&5). Should the manager buy the machine?

Total savings are $365k by spending $300k today; however the PV of the cost savings is $284,679. Consequently, the NPV of the new machine is -$15,321 thus the manager should not purchase the new machine.

An analyst for a major apparel company estimates that the demand for its raincoats is given by ln Qdx = 10 - 1.2 ln Px + 3 ln R - 2 ln Ay where R denotes the daily amount of rainfall and Ay represents the level of advertising on good Y. What would be the impact on demand of a 10%increase in the daily amount of rainfall? What would be the impact of a 10% reduction in the amount of advertising directed toward good Y? Can you think of a good that might be good Y in this example?

We know that for log-linear demand functions, the coefficient of the logarithm of a variable gives the elasticity of a demand with respect to that variable. Thus, the elasticity of demand for raincoats with respect to rainfall is Qqx, R = BR = 3 Eqx, R = BR = %changeQxd/%changeR 3 = %changeQxd/10 Solving this equation yields 30. In other words, the 10% increase in rainfall will lead to a 30% increase in the demand for raincoats. To examine the impact on the demand for raincoats of a 10% reduction in advertising spent on good Y, the elasticity of demand for raincoats with respect to advertising direct toward Y is Ex,Ay = BAy = -2 Eqx, Ay = BA = %changeQxd/%changeAy -2 = %changeQxd/-10 Solving this equation yields %changeQdx = 20. In other words, 10% reduction in advertising leads to a 20% increase in the demand for raincoats. Perhaps good Y is umbrellas.

B(Y) = 300(Y) - 6Y^2 C(Y) = 4Y^2 MB = 300 - 12 Y MC = 8Y What is the max levels of net benefits and the level of Y that will yield that result?

Y = 15 NMB = 2,250

The demand for widgets (x) is given by Px = 160 - 4x. The production of widgets has the following average variable costs: AVC = 2x - 20 and FC = 162 Calculate the output level of widgets that: a) max TR b) Min ATC of widgets c) Min TC of widgets d) Max profits

a) 20 widgets b) 9 widgets c) 5 widgets d) 15 widgets

Given that the total cost function is : TC = 100Q - Q^2 + 1/3Q^3 where Q = rate of output and TC = total cost a) Determine the marginal cost and average cost functions. b) Calculate the output level that minimizes average cost. c) Calculate the output level that minimizes marginal cost.

a) MC = 100 - 2Q + Q^2 and Av cost = 100 - Q + 1/3Q^2 b) 1.5 units c) 1 unit

If the interest rate is 10%, growth rate is 5% and profits of a firm are $100 m ... a) What is the value of the firm? b) What is the value of the firm immediately after it oays the amount equal to its profits?

a) PV (firm) = $2,200 m b) PV (ex-dividend firm) = $2,100 m