Question

1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of...

1. A firm production function is given by q(l,k) = l0.5·k0.5, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used. This firm profit function is π = p·q(l,k) – w·l – v·k, where p is the price of output, w the wage rate of labor and v the rental rate of capital. In the short-run, k = 100. This firm hires its profit maximizing level of labor input. In the short-run, this firm demand equation for labor l is a factor a of (p/w)2: l = a (p/w)2. In this specific case, factor a is equal to [a]. (HINT: This is unconstrained profit maximization problem. Set your first order condition by taking the derivative of your profit function with respect to l equal to zero, assume the second order condition is satisfied, and solve for l. NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)

2. An individual utility function is given by U(c,h) = c·h, where c represents consumption during a typical day and h hours of leisure enjoyed during that day. Let l be the hours of work during a day, then l + h = 24. The real hourly market wage rate the individual can earn is w = $20. This individual receives daily government transfer benefits equal to n = $100. For the graphical analysis of this individual’s utility maximization problem, consumption c is plotted on the vertical axis and hours of leisure h is plotted on the horizontal axis. The y-intercept for this individual’s full income constraint is [y]. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
2. An individual utility function is given by U(c,h) = c·h, where c represents consumption during...
2. An individual utility function is given by U(c,h) = c·h, where c represents consumption during a typical day and h hours of leisure enjoyed during that day. Let l be the hours of work during a day, then l + h = 24. The real hourly market wage rate the individual can earn is w = $20. This individual receives daily government transfer benefits equal to n = $100. For the graphical analysis of this individual’s utility maximization problem,...
14. A firm’s production function is Q = 12*L0.5*K0.5. Input prices are $36 per labor unit...
14. A firm’s production function is Q = 12*L0.5*K0.5. Input prices are $36 per labor unit and $16 per capital unit. The product’s price is P = $10. (Given: MP(L) = 6*L-0.5*K0.5; and MP(K) = 6*L0.5*K-0.5) In the short run, the firm has a fixed amount of capital, K = 9. Calculate the firm’s profit-maximizing employment of labor. (Note: short term profit maximization condition: MPR(L) = MC(L) ) In the long run, suppose the firm could adjust both labor and...
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of...
A firm’s production function is Q(L,K) = K^1/2 + L. The firm faces a price of labor, w, and a price of capital services, r. a. Derive the long-run input demand functions for L and K, assuming an interior solution. If the firm must produce 100 units of output, what must be true of the relative price of labor in terms of capital (i.e. w/r) in order for the firm to use a positive amount of labor? Graphically depict this...
An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x...
An individual utility function is given by U(x,y) = x·y1/2. This individual demand equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to [a]. (NOTE: Write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero and trailing zeros when needed.)
Consider a firm using the production technology given by q = f(K, L) = ln(L^K) If...
Consider a firm using the production technology given by q = f(K, L) = ln(L^K) If capital is fixed at K = 2 units in the short run, then what is the profit maximizing allocation of output if the price of output and respective input prices of labor and capital are given by (p, w, r) = (2, 1, 5)?
Suppose an agricultural firm has the production function: f(l; k; a) = l^(1/4) * k^(1/4) *...
Suppose an agricultural firm has the production function: f(l; k; a) = l^(1/4) * k^(1/4) * a^(1/4) where the price of labor is w, the price of capital is r and acreage (a) has price s. (a) Verify that this is a valid production function. (b) Solve the rm's cost minimization problem for the conditional input demands, cost function, average cost function, and marginal cost function. (c) Suppose that there was a tax on one or more inputs. For each...
A firm produces an output with the production function Q=K*L2, where Q is the number of...
A firm produces an output with the production function Q=K*L2, where Q is the number of units of output per hour when the firm uses K machines and hires L workers each hour. The marginal product for this production function are MPk =L2 and MPl = 2KL. The factor price of K is $1 and the factor price of L is $2 per hour. a. Draw an isoquant curve for Q= 64, identify at least three points on this curve....
3. Consider the production function, Q = [L0.5 + K0.5] 2 . The marginal products are...
3. Consider the production function, Q = [L0.5 + K0.5] 2 . The marginal products are given as follows: MPL = [L0.5 + K0.5] L-0.5 and MPK = [L0.5 + K0.5] K-0.5 and w = 2, r = 1. A). what is the value of lambda B). Does this production function exhibit increasing, decreasing or constant returns to scale? C).Determine the cost minimizing value of L D).Determine the cost minimizing value of K E).Determine the total cost function F).Determine the...
Price taking firm with a P = $5 with the following production function Q = f(L,K)...
Price taking firm with a P = $5 with the following production function Q = f(L,K) = 20 x L^0.25 x K^0.5 w = $20 r = $10 What is the profit maximising input combination? With step by step working please
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L...
A firm’s production function is given by Q = 5K1/3 + 10L1/3, where K and L denote quantities of capital and labor, respectively. Derive expressions (formulas) for the marginal product of each input. Does more of each input increase output? Does each input exhibit diminishing marginal returns? Prove. Derive an expression for the marginal rate of technical substitution (MRTS) of labor for capital. Suppose the price of capital, r = 1, and the price of labor, w = 1.   The...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT