ECON105A Final

A firm has the production function f(x, y) = 20x3/5 y2/5. The slope of the firm's isoquant at the point (x, y) = (20, 40) is (pick the closest one) -3. -0.67. -1.50. -0.50. -0.25.

-3.

A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4x1/2. The price of output is $12 and the factor price is $3. The amount of the factor that the firm demands is 64. 16. 60. 8. None of the above.

64.

A competitive firm produces output using three fixed factors and one variable factor. The firm's short-run production function is q = 305x -2x2, where x is the amount of variable factor used. The price of the output is $2 per unit and the price of the variable factor is $10 per unit. In the short run, how many units of x should the firm use? 37 150 21 75 None of the above.

75

If a firm moves from one point on a production isoquant to another point on the same isoquant, which of the following will certainly not happen? A change in the level of output A change in the ratio in which the inputs are combined A change in the marginal products of the inputs A change in the technical rate-of-substitution A change in profitability

A change in the level of output

If Green Acres Turf Farm's total cost of producing acres of sod is TC =5Q2 + 25Q + 40, the marginal cost of producing the 10th acre of sod is $125. $40. $25. $75. $275.

$125.

Using existing plant and equipment, Priceless Moments Figurines can be manufactured using plastic, clay, or any combination of these materials. A figurine can be manufactured by F = 4P + 2C, where P is pounds of plastic and C is pounds of clay. Plastic costs $2 per pound and clay costs $5 per pound. What would be the lowest cost of producing 40,000 figurines? $20,000 $100,000 $60,000 $10,000 $40,000

$20,000

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{1.5C, 3P}, where M, C, and P are pounds of manicotti, cheese, and pasta respectively. If cheese costs $3 per pound and pasta costs $1 per pound, how much would it cost to produce 10 pounds of manicotti in the cheapest way possible? $3.33 $20 $23.33 $35 $10

$23.33

Nadine has a production function 2x1 + x2. If the factor prices are $8 for factor 1 and $5 for factor 2, how much will it cost her to produce 70 units of output? $1,470 $280 $350 $910 $315

$280

In the short run, a firm which has production function f(L, M) =4L1/2M1/2 must use 4 machines. If the cost of labor is $4 per unit and the cost of machines is $10 per unit, the short-run total cost of producing 72 units of output is $504. $288. $720. $728. $364.

$364.

The inverse demand function for cases of whiskey defined by p = 186 - 6q, and the inverse supply function is defined by p = 90 + 2q. Originally there was no tax on whiskey. Then the government began to tax suppliers of whiskey $32 for every case they sold. How much did the price paid by consumers rise when the new equilibrium was reached? It rose by $32. It rose by $24. It rose by $22. It rose by $34. None of the above.

It rose by $24.

If output is produced according to Q = 4L + 6K, the price of K is $24, and the price of L is $20, then the cost-minimizing combination of Kand L capable of producing 72 units of output is L = 9 and K = 6. L = 20 and K = 24. L = 18 and K = 12. L = 0 and K = 12. L = 18 and K = 0.

L = 0 and K = 12.

If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $40, then the cost-minimizing combination of K and L capable of producing 64 units of output is L = 16 and K = 1. L = 2 and K = 8. L = 2 and K = 2. L = 32 and K = 32. L = 1 and K = 16.

L = 2 and K = 8.

A firm has the production function Q = X1/21X2. In the short run it must use exactly 15 units of factor 2. The price of factor 1 is $75 per unit and the price of factor 2 is $2 per unit. The firm's short-run marginal cost function is MC(Q) = 2Q/3. MC(Q) = 30Q1/2. MC(Q) = 30 + 75Q2. MC(Q) = 2Q. MC(Q) = 15Q1/2.

MC(Q) = 2Q/3.

A production function has well-defined marginal products at every input combination. If factor x is shown on the horizontal axis and factor y is shown on the vertical axis, the slope of the isoquant through a point (x*, y*) is the negative of the ratio of the marginal product of x to the marginal product of y.

True

If the price of the output of a profit-maximizing, competitive firm rises and all other prices stay constant, then the firm's output cannot fall.

True

If there are increasing returns to scale, then average costs are a decreasing function of output.

True

The cost function C(y) = 10 + 3y has marginal cost less than average cost for all levels of output.

True

The fraction of a $t quantity tax paid by buyers rises as demand becomes less elastic.

True

The production function f(x, y) = x + y has constant returns to scale.

True

A firm produces Ping-Pong balls using two inputs. When input prices are ($15, $7) the firm uses the input bundle (17, 71). When the input prices are ($12, $24) the firm uses the bundle (77, 4). The amount of output is the same in both cases. Is this behavior consistent with Weak Axiom of Cost Minimization (WACM)? Yes. No. It depends on the level of the fixed costs. We have to know the price of the output before we can test WACM. It depends on the ratio of variable to fixed costs.

Yes.

The production function Q = 50K0.25L0.25 exhibits increasing returns to scale. constant returns to scale. decreasing returns to scale. increasing, then diminishing returns to scale. negative returns to scale.

decreasing returns to scale.

A firm has the production function f(x, y) = x0.90y0.80. This firm has constant returns to scale. decreasing returns to scale and diminishing marginal products for factor x. decreasing returns to scale and increasing marginal product for factor x. increasing returns to scale and decreasing marginal product of factor x. None of the above.

increasing returns to scale and decreasing marginal product of factor x.

A firm has a production function f(x, y) = 1.40(x0.60 + y0.60)2 whenever x > 0 and y > 0. When the amounts of both inputs are positive, this firm has increasing returns to scale. decreasing returns to scale. constant returns to scale. increasing returns to scale if x + y > 1 and decreasing returns to scale otherwise. increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

increasing returns to scale.

In any production process, the marginal product of labor equals the value of total output minus the cost of the fixed capital stock. the change in output per unit change in labor input for small changes in the amount of input. total output divided by total labor inputs. total output produced with the given labor inputs. the average output of the least-skilled workers employed by the firm.

the change in output per unit change in labor input for small changes in the amount of input.

A competitive firm produces a single output using several inputs. The price of output rises by $4 per unit. The price of one of the inputs increases by $2 and the quantity of this input that the firm uses increases by 8 units. The prices of all other inputs stay unchanged. From the weak axiom of profit maximization we can tell that the output of the good must have increased by at least 4 units. the inputs of the other factors must have stayed constant. the output of the good must have decreased by at least 2 units. the inputs of at least one of the other factors must have decreased by at least 8 units. the inputs of at least one of the other factors must have increased by at least 8 units.

the output of the good must have increased by at least 4 units.

The production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? x1 = x2. x1 = 0.50x2. x1 = 2x2. x1 = 24x2. We can't tell without knowing the price of the output.

x1 = 2x2.

If a competitive firm's technology exhibits constant returns-to-scale, then the firm has infinitely many profit-maximizing production plans.

False

If the production function is f(x1, x2) = x1x2, then there are constant returns to scale.

False

If the supply curve is vertical, then the quantity supplied is extremely sensitive to the market price.

False

Marginal cost (MC) is the slope of the variable cost function, not the slope of the total cost function.

False

The cost function c(w1, w2, y) expresses the cost per unit of output of producing y units of output.

False

The incidence of a quantity tax depends on whether the tax is levied on buyers or on sellers.

False

The marginal cost curve passes through the minimum point of the average fixed cost curve.

False

When the market price is below the equilibrium price, there is an excess of quantity supplied over quantity demanded.

False

The following relationship must hold between the average total cost (ATC) curve and the marginal cost curve (MC): If MC is rising, ATC must be rising. If MC is rising, ATC must be greater than MC. If MC is rising, ATC must be less than MC. If ATC is rising, MC must be greater than ATC. If ATC is rising, MC must be less than ATC.

If ATC is rising, MC must be greater than ATC.

Two firms, Wickedly Efficient Widgets (WEW) and Wildly Nepotistic Widgets (WNW), both produce widgets, using the same production function y = K1/2L1/2, where K is the amount of labor used and L is the amount of capital used. Each company can hire labor at $1 per unit of labor and capital at $1 per unit. Each company produces 10 widgets per week. WEW chooses its input combinations to produce in the cheapest way possible. Although it produces the same output per week as WEW, WNW is required by its dotty CEO to use twice as much labor as WEW. How much higher are WNW's total costs per week than WEW's? $5 $10 $15 $2.50 $2

$5

An orange grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x1, x2}, where x1 and x2 are the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are w1 = $5 and w2 = $2,respectively. The minimum cost of producing 140 units is therefore $980. $630. $1,400. $280. $700.

$630.

The production function is given by f(x) = 4x1/2. If the price of the commodity produced is $60 per unit and the cost of the input is $20 per unit, how much profit will the firm make if it maximizes profits? $1,444 $705 $720 $358 $363

$720

The production function is f (L, M) = 4L1/2M1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $64 per unit and the cost of using machines is $1 per machine, then the total cost of producing 20 units of output is $80. $650. $20. $320. $40.

$80.

When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1-N/200 bushels of corn. If the price of corn is $1 per bushel and the price of fertilizer is $.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits? 84 328 320 160 200

160

The demand for pickles is given by p = 167 - 3q and the supply is given by p = 5 + 6q. What is the equilibrium quantity? 15 23 113 18 None of the above.

18

The inverse demand function for apples is defined by the equation p= 214 - 5q, where q is the number of units sold. The inverse supply function is defined by p = 7 + 4q. A tax of $36 is imposed on suppliers for each unit of apples that they sell. When the tax is imposed, the quantity of apples sold falls to 23. 14. 17. 19. 21.

19.

Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs. (1) y = K1/2L1/3. (2) y = 3K1/2 L1/2. (3) y = K1/2 + L1/2. (4) y = 2K + 3L. 1, 2, and 4 2, 3, and 4 1, 3, and 4 2 and 3 2 and 4

2 and 4

A competitive firm's production function is f(x1, x2) = 12x1/21 +4x1/22. The price of factor 1 is $1 and the price of factor 2 is $2. The price of output is $4. What is the profit-maximizing quantity of output? 304 608 300 612 292

304

A firm has fixed costs of $4,000. Its short-run production function is y = 4x1/2, where x is the amount of variable factor it uses. The price of the variable factor is $4,000 per unit. Where y is the amount of output, the short-run total cost function is 4,000/y + 4,000. 8,000y. 4,000 + 4,000y. 4,000 + 250y2. 4,000 + 0.25y2.

4,000 + 250y2.

A firm has the short-run total cost function c(y) = 4y2 + 100. At what quantity of output is short-run average cost minimized? 5 2 25 0.40 None of the above.

5

The production function is given by F(L) = 6L2/3. Suppose that the cost per unit of labor is $16 and the price of output is $16. How many units of labor will the firm hire? 192 64 32 128 None of the above.

64

The inverse demand function for lemons is defined by the equation p= 120 - 11q, where q is the number of crates that are sold. The inverse supply function is defined by p = 8 + 3q. In the past there was no tax on lemons but now a tax of $84 per crate has been imposed. What are the quantities produced before and after the tax was imposed? 4 crates before and 3 crates after 8 crates before and 2 crates after 16 crates before and 5 crates after 16 crates before and 5 crates after None of the above.

8 crates before and 2 crates after

Deadweight loss due to a quantity tax falls as either market demand or market supply becomes more elastic.

False

The UJava espresso stand needs two inputs, labor and coffee beans, to produce its only output, espresso. Producing an espresso always requires the same amount of coffee beans and the same amount of time. Which of the following production functions would appropriately describe the production process at UJava, where B represents ounces of coffee beans, and L represents hours of labor? Q = B0.60L0.40. Q = B/2 + L/2. Q = min{2B, 60L}. Q = 0.5B + 0.5L0.5.

Q = min{2B, 60L}.

The inverse demand function for eggs is p = 84 - 9q, where q is the number of cases of eggs. The inverse supply is p = 7 + 2q. In the past, eggs were not taxed, but now a tax of 33 dollars per case has been introduced. What is the effect of the tax on the quantity of eggs supplied? Quantity drops by 2 cases. Quantity drops by 3 cases. Quantity drops by 6 cases. Quantity drops by 4 cases. None of the above.

Quantity drops by 3 cases.

The inverse demand function for cigars is defined by p = 240 - 2q, and the inverse supply function is defined by p = 3 + q. Cigars are taxed at $4 per box. The after-tax price paid by consumers rises by more than $2, and the after-tax price received by suppliers falls by less than $2. The after-tax price paid by consumers goes up by less than $2, and the after-tax price received by suppliers rises. Consumers and suppliers share the cost of the tax equally. The after-tax price paid by consumers rises by $4, and the after-tax price received by suppliers stays constant. The after-tax price paid by consumers rises by less than $2, and the after-tax price received by suppliers stays constant.

The after-tax price paid by consumers rises by more than $2, and the after-tax price received by suppliers falls by less than $2.

The production function of a competitive firm is described by the equation y = 8X1/21X1/22. The factor prices are p1 = $1 and p2 = $4 and the firm can hire as much of either factor as it wants at these prices. The firm's marginal cost is constant and equal to 0.50. constant and equal to 3. increasing. decreasing. None of the above.

constant and equal to 0.50.

A firm produces one output using one input. When the cost of the input was $3 and the price of the output was $3, the firm used 6 units of input to produce 18 units of output. Later, when the cost of the input was $7 and the price of the output was $4, the firm used 5 units of input to produce 20 units of output. This behavior is consistent with WAPM. is not consistent with WAPM. is impossible no matter what the firm is trying to do. suggests the presence of increasing returns to scale. suggests the presence of decreasing returns to scale.

is not consistent with WAPM.