Suppose the production function is given as ? = √??. Suppose also that the price of...

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