Numerical Example: A firm's optimization problem Given: production function: y-10 / KN capital stock K -9,...
Numerical Example: A household's optimization problem Given: household's utility: U(C,e) 15 In l 16 In C total time endowment h 9, real wage w7.5, taxes T 20 and capital income T30 Follow these steps: write down the budget constraint o substitute the BC into the objective function o optimize (write down the FOC) o find C, and labour supply N
Econ 10A: Problem Set 9 (1) A firm's production function is P(L, K) 2LV2K. Find the long-run profit-maximizing values of Land K when the wage for labor is w $10, the rental rate for capital is r $20, and the price of output is p $40.
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...
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...
Assume the following production function: Y=8K^0.3N^0.7 If the capital stock is K = 30, and the prevailing wage rate is w* = $25, find the full employment. (can you please anwering with the detailed calculation steps? Thanks!)
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...
Question 2: Firms Consider a firm that produces output Y from capital K and labour N using the production iechoolopy Y KNdThe f's capital endowcnt is piven as K 50 Labour is hired to maximize profits. At a wage rate w, the firm's labour costs are wN The firm's profit (as a function of N is therefore 1. Find the firm's labour demand function by maximizing profits and solving the fist order condition for the wage rate w. 2. Plot...
6. A firm's production function is given by q 20(EV2 +K2), where q is output and E and K are amounts of labour and capital, respectively. If the wage rate is w $15 per hour and the price of capital is r $60 per hour, what is the firm's profit maximizing capital/labour ratio? A. K/E 20 D. K/E 4 E. K/E = 16 B. K/E 200 C. K/E 1/2
A firm's Cobb-Douglas production function for output x is f(l,k)= 25/5k5, where / (labour) and k (capital) 9. are variable inputs costing w (wage rate) and r (rental cost of capital) each per unit (a) Follow the two-step (indirect) method' and begin by setting up the firm's cost- minimisation problem and deriving the three first-order conditions (FOC8) (4 marks) 2(wr)2 x2 (where, to be clear, (c) The cost function derived from the FOC8 above is c(w,r,x) 3125 1 5 the...
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.