ECON 310 Lecture 3: p310x3

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taupeserval94

10 May 2017

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What is the instantaneous marginal product at l=4: on a separate graph draw the marginal product and average product. L=4 and l=8: draw the cost function of this firm. Include the values for q=4 and q=8: on a separate graph, draw the marginal cost (using instantaneous calculation) and average cost curves. Draw the supply curve: how much will this firm offer to the market if the price of output is . What are the profits of the firm: (12 points) isoquants, isocost, and cost functions. For this problem, consider firm that uses a cobb-douglas production function of the form: And which faces the following prices: wage = /unit , rental rate on capital = /unit. [note: you do not need to derive your solutions. Cobb-douglass for the slope of the isoquants: draw the isoquant for a quantity of 4. Explain: calculate the cost function of this firm at the given input prices with c as a function of q.

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4. (8 points) Assume that a firm has the following production function: q = f(K,L). Further assume that the isoquants for this function are convex. The wage rate is $4/hour, and the rental rate is $6/hour. a. (4 pts) In the LR, the firm produces its output where the marginal product of labor is 8, and the marginal product of capital is 9. Is the firm producing its output in an economically efficient manner? Why or why not? b. (4 pts) Should the firm change its input mix? If so, should they use more L (and less K) or more K (and less L)?

fuchsiawhale231

This is due today!! Thank you!!

Consider a firm with production function f(L, K)=2L+6K. Assume that capital is fixed at K=6. Then, the amount of labor necessary to produce q units is?

A		L(q,6)= q-12
B		L(q,6)= q/18-5
C		L(q,6)= q/2-18
D		L(q,6)= 3q/5-2
E		L(q,6)= q²/2-12

Consider a firm with production function f(L, K)= 4L^2/3K^1/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=4 and the price of labor w=2. Then, the average cost of producing q units is?

A		AC(q)= 4/q+q^1/2/4.
B		AC(q)= 2/q+1/4q^1/3.
C		AC(q)= 2/3q+1/q^1/3.
D		AC(q)= 1/3q+q^1/2.
E		AC(q)=8/q+2q^1/2.

Consider a firm with production function f(L, K)=3L^1/3K^2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the cost of producing q units is?

A		C(q)=3+q²/9.
B		C(q)=10+q³.
C		C(q)=5+q³/9.
D		C(q)=2/3+q²/3.
E		C(q)=1/3+q³/3.

peardinosaur914

3. A firm has a long-run production function:

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run?

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

salmonhyena380

ECON 310 Lecture 3: p310x3

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