10 pt 2 Assume a production function exists and is Q = (K^.25 L^.75) let a...
10 pt 2
Assume a production function exists and is Q = (K^.25 L^.75)
let a firm have a total of $1,100 to spend on labor and capital. Let price of labor equal $5 and price of capital equals $10
1) calculate the optimal values of Q, and the new isoquants and plot the LR expansion path.
2) Keeping K at 25, and letting L vary, plot the SR expansion path and the TPL curve
Homework Answers
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10 pt 2
Assume a production
function exists and is Q = (K^.25 L^.75)
let a...
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)
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit. a. Determine the current total cost for 100 units,...
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S:...
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S: where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 1 kg of kiwi fruits and 3 hours of labour, he can produce 1 bottle of juice a) Draw isoquants for q, q 2 and q 3 on a diagram with labour on horizontal axis and kiwi fruits on vertical b) Let the price...
Using the production function Q = ( and output levels of Q=2, Q=4, Q=6 A). Suppose...
Using the production function Q = (
and output levels of Q=2, Q=4, Q=6
A). Suppose the price of L and K is $3/hr. On a graph show
isocost lines corresponding to total costs of $12, $24, and $36.
Using isoquants and isocost lines, locate three points on the
expansion path and draw the expansion path. Show your
calculations.
B). Using the three points on the expansion path, calculate the
firm's long run total and average costs at each of...
7. An Italian sausage maker’s production function is Q = 8k.25 L.25 MPK = 2K-.75 L.75,...
7. An Italian sausage maker’s production function is Q = 8k.25 L.25 MPK = 2K-.75 L.75, MPI = 6K.25 L-.25 • Determine the firm’s short-run cost equation (assume K is the fixed input). • Determine the firm’s long-run cost equation • If the price of K is $4 and the price of L is $24 and K is fixed at 32 units determine the K, L, Q where the short-run cost equals the long-run cost. What is the cost?
A company has the production function Q = min{K, L}. The price of capital is $50...
A company has the production function Q = min{K, L}. The price of capital is $50 per unit while the price of labor is $75 per unit. On a graph, plot isoquants for quantities 10, 20, and 30, as well as the isocost line for a quantity of 20. Note the cost-minimizing levels of capital and labor on your graph given the target production level of 20 units. The McCue Corporation is a house-painting business. For a standard-sized house, it...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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?...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. Wha...
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. What combination of labor and capital minimizes the cost of producing any output? To produce a given level of output q, how many units of L and K are needed? Express the optimal inputs choices L(q) and K(q) as functions of the level of output q
Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function 1S: where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 1 kg of kiwi fruits and 3 hours of labour, he can produce 1 bottle of juice a) Draw isoquants for q, q 2 and q 3 on a diagram with labour on horizontal axis and kiwi fruits on vertical b) Let the price...
Using the production function Q = (
and output levels of Q=2, Q=4, Q=6
A). Suppose the price of L and K is $3/hr. On a graph show
isocost lines corresponding to total costs of $12, $24, and $36.
Using isoquants and isocost lines, locate three points on the
expansion path and draw the expansion path. Show your
calculations.
B). Using the three points on the expansion path, calculate the
firm's long run total and average costs at each of...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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?...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
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