FInd the profit maximizing levels of K and L as functions of r,w, and p. b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?
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Consider two firms that produce a single output good,y, using two inputs :Capital, K , and labor, L, the prices of each unit of capital and labor are r and w,respectively. The output good y sells for $p per unit.
Firm A's production function is y = fa(K,L) = K1/4L1/4. The profit function is equals to : K1/4L1/4 - rK -wL.
a) FInd the profit maximizing levels of K and L as functions of r,w, and p.
b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?
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- Problem #1 Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. the prices of each unit of capital and labor are r and w, The output good y sells for $p per unit. Firm A’s production function is y = fA(K,L) = K1/4 L1/4. The profit function is thus: ðA(K,L) = K1/4 L1/4 – rK -wL Find the profit maximizing levels of K and L as functions of r, w, and p. Suppose that r = w = $1 and p = $4. What is the profit maximizing level of output, y ?1. Consider two firms that produce a single output good, y, using two inputs: Capital, K, and labor, L. the prices of each unit of capital and labor are r and w, respectively. The output good y sells for $p per unit. Firm A's production function is y = fa(K,L) = K4 L14. The profit function is thus: DA(K,L) = K4 L'1/4 – rK -wL a. Find the profit maximizing levels of K and L as functions of r, w, and p.Suppose that r= w=$1 and p= $4. What is the profit maximizing level of output y?
- Consider the production functions of three different Firms utilizing inputs labor (L) and capital (K) in producing goods X, Y, and Z given below. The three firms face the same fixed price for labor and capital at 5 per unit and 10 per unit, respectively. X = KL2 – L3; Y = 10K1.5L0.5; Z = K0.5L0.5 Mathematically show at what stage of production Firm X will experience the law of diminishing marginal productivity/ returns if it chooses to employ 30 units of capital. Graphically illustrate your resultsConsider the production functions of three different Firms utilizing inputs labor (L) and capital (K) in producing goods X, Y, and Z given below. The three firms face the same fixed price for labor and capital at 5 per unit and 10 per unit, respectively. X = KL2 – L3; Y = 10K1.5L0.5; Z = K0.5L0.5 a. Derive the short-run cost function of Firm Z if 25 units of capital are employed. Suppose that good Z is sold at a perfectly competitive price of 10 per unit, calculate Firm Z’s profit and discuss if the Firm Z should continue to operate.b. Derive the long-run cost function of Firm YA firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is PQ= MRQ = d = $40. The prices of L and K are PL = $6 and PK= $12. Suppose K is fixed at K =10. Use Excel Solver or otherwise to find the profit-maximizing quantity (Q).
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