Question

Suppose the production function is given as ? = √??. Suppose also that the price of labor ? = 10 and the price of capital ? = 40
1) Derive the equation of the isoquant corresponding to this production function?

2) What type of return to scale does this production exhibit?

3) Does this production function exhibit a diminishing MRTS? Why?

4) Based on this production function, is the law of diminishing marginal returns satisfied?

5) Derive the demand curves for labor and capital.

6) Derive the long run total cost function

7) What is the long run average and marginal cost functions?

8) Calculate the output elasticity of total cost? Based on your calculated elasticity, what is the type of return to scale that the producer faces.

9) Suppose that capital is fixed at a level ? ̅ . What is the short run total cost function for this production function.

10) What is the short run average variable cost and short run average fixed cost functions?

please show your work on a paper, thanks

Answer 1

Suppose the production function is given as ? = √??. Suppose also that the price of labor ? = 10 and the price of capital ? = 40
1) Derive the equation of the isoquant corresponding to this production function?

Equation of isoquant is identical to the production function

Q=LK

2) What type of return to scale does this production exhibit?

Let us increase both inputs by N

01- (NXL) Y(N-K) 91 - H x W x ( x ) SL = N?xLK 01= N2x8 It = NP)N Therefore, increasing both inputs by N times increases output by more than N times, there is increasing returns to scale. 3) Does this produchon function exhibit a diminishing ARTS ? why? MIRTS = APL/APK MPL =20/2L =K MPK = ƏQLƏR =L MRTS - R/L Therefore, as L increases, MRTS decreases, revealing a diminishing MRTS in labor. GBased on this production function, is the law of diminishing marginal return satisfied ? → MPL=k - mpk=L So. The MPL is independent of K. The MP12 is independent of L .: Diminishing returns to scale is not satisfied

s! Derive the demand curves for labor and capitali or Toro Costis minimized when MRTS > W KIL = 1%40 = 44 L=4R Substituting in production function G = GR XK - 4K K²=814 k=Q0.5/2 L = 4K = 4 XQ 12 = 2*805 6) Derive the long run total cost function. Total Lost C=WL + rk = 10L +40K c = (10*2 x Qº$ ) + 40x(Q2572) C = 204 205+ 20xQ0.5 c=40 x Qor 7) what is the long run average and margincy cost functions ? + Average cost = C19 - 40700.5 marginal cost = dC/dQ = 40x0.5/80.5 +20%8051