Homework Answers
It is an example of production function with fixed proportion of inputs
a)
We need 3 wheels (W) and 1 Frame (F) to produce one unit of Tricycle. So, production function is given by
Q(F, W)=min(F, W/3)
b)
We need 3 wheels (W) and 1 Frame (F) to produce one unit of Tricycle. So, Cost function is given by
TC(Q,PF,PW)=1*PF*Q+3*PW*Q=(PF+3PW)*Q
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2. Tricycles must be produced with 3 wheels and 1 frame for each tricycle. Let l...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w, r, and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p.
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital,...
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is...
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the...
Consider a production function Q=Q(K,L)=6K^(1/2)L^(1/3) with K as capital and L as labor input. Let the price per unit of output be P=$0.50, the cost or rental rate per unit of capital be r=$0.10 and let the price (wage rate) of labor be w=$1. a) find the profit max level of K and L and check with second order condition (my answer was L=3.375 and K=1.5) b) Find max profit (I got profit=1.986)
II. A simple economy with two factor inputs and two outputs. Let there be two factor...
II. A simple economy with two factor inputs and two outputs. Let there be two factor inputs: land denoted T and labor denoted L. The resource endowment of T is Tº = 8; the resource endowment of L is Lº = 8. Let there be two goods: z and y. Robinson has a utility function u(x,y) := xy. The prevailing wage rate of labor is w, and the rental rate on land is r. Good is produced in a single...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
(a) Let L and L' be two lines in R3. 1:*2 =12-21 Lt -1 5 -2...
(a) Let L and L' be two lines in R3. 1:*2 =12-21 Lt -1 5 -2 -1 2-5 -4. Determine if the lines intersect at a point. If the , write down the three coordinates of the intersection point in the three boxes below. If they do not, enter the three letters D, N, E, one in each box below (for Does NotExist) (b) An insect is flying along a path r(x,y,z) = (x(t), y(t), z(t)) in a room where...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
. Consider the production function: f(K,L)=KLA. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w, r, and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p.
Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function.
7. Suppose a firm's production function is Q-min(L,K). (This means the level of O produced is the smaller of L and K) a. Graph some isoquants for this firm. b. Let w = 2, r= 1, and suppose the firm's expenditures are C-12. What are the firm's demands for L and K? What is the share of labor in the cost of output? c. Now let w rise to 3. What are the firm's new demands for L and K?...
II. A simple economy with two factor inputs and two outputs. Let there be two factor inputs: land denoted T and labor denoted L. The resource endowment of T is Tº = 8; the resource endowment of L is Lº = 8. Let there be two goods: z and y. Robinson has a utility function u(x,y) := xy. The prevailing wage rate of labor is w, and the rental rate on land is r. Good is produced in a single...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
(a) Let L and L' be two lines in R3. 1:*2 =12-21 Lt -1 5 -2 -1 2-5 -4. Determine if the lines intersect at a point. If the , write down the three coordinates of the intersection point in the three boxes below. If they do not, enter the three letters D, N, E, one in each box below (for Does NotExist) (b) An insect is flying along a path r(x,y,z) = (x(t), y(t), z(t)) in a room where...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
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