Question

1. Consider the figure below illustrating an isoquant and isocost line for the ABC Fruit Company's production of guavas: x 6 a. [2 pts] Given the isocost line shown above, if the wage rate (w) is 2 and total cost is 12, what is the price of capital, r?

Answer 1

line . and ka 6 a The iso quant is tangent to the Iso cost at point A tie at optimal bundle (3,6) Where c = 3 ond K-6 and k=6 Now, wage rate (W) = 2 and to tal cost (e) = 12 Now Equation of iso cost line .. e= wat ok Substituting w=2; e = 12, L=3 We gets 12 = 12x3) +68. =) 12 = 6 + 60 ; 6 = 69 =) = 1 Scanned' with CamScanner

да Pu bike •1. . I b2 suppose that the marginal procact of labor MPL=6: marginal product of capital mPk 3 at point e. At point B the amont of than the amout of labor at point Labor is lown than a at point B will be higher than the the B At point figue. A einst he A. Hence MPL at point B will be MPL at point A. At point B level of capital is higher than the level of capital at point A, Hunce mpk at point B. will be lown them the MPK at point A : - L . Now suppose were told that ABC frent's production function takes the form Q = Lk . Now, Marginal Product of labor (MPL) = 2 20 =k . and Marginal product of capital (MP x) = 20 =L Hence, the Marginal rate of technical substitution of įfor ak MOL - мек MRTS = , K Now, increasing both L and K by a scalas constant z we get, Q (24, 2K) = (22)(2k)= 2*2= 2*& tice, increasing both L and k by Z, increase out put a by Z². Hunce this function exhibits [cs increasing returns to scale. CamScanner

- a Now suppose we learn only that . the wage is nine times as lange as r. ie w=ar, we know 8=1, hence W=(9x1) = 9 Now, optimal input min condition will be! - MPL MPK =) A = 9 ) K = 9L Now subschituting K= 92 in the production function we get, Q = LK the we want to produce Q = 36 .. Hace 36 LK : Substituting k=qL we get, . 36=2X OL. = 36 = 92² =) < ² = 4 = 1=2 and as k=qL=(9x2 =18 Hace, choice of k= 18 . . choice of L = 2 Scanned with CamScanner

e suppose w falls so that it eques mi je way. We know re 1 hence w= 1 Now optimal input min condition will be MPL = 8 MPK MPK 2) Ķ . I - KEL Substituting k=2 in the production function 36=kL we get, we get, 36=kL 3 36 = (kxk) =) K= 36 s) K-6 on, k= L, hence L= 6 choice of k=E 6 Choice of 2 = 6 a production function and with in put min Condition with . [= x= 1; the same Optimal will ber =) -5 -) KEL Now substituting K= L in the Production fonction Q = KL we at Q=KL = (kxk) .. = Q = K2 ..=) k ra=Q² Scanned with CamScanner

. AS LEK , hence L. Q 12 Now, choice of Ki Q/ Choice of i= Q/ Now him's cost for it on! es WL+MK substituting . W =r=1 and L=Q" and K= Q² we get, cs (1x Q%)+(2 x0h) a) e=2Q/ Now, Now cost elasticity of output Now . c = 20% - de la = (2x ) Q ² Q-² Now substituting de = Q-², (= 20% : ü cost elasticity of outbut we get, = Q-/. Q a ZQ/ as Q-²2 Q/2 = 0.5 As the value of cost elasticity is ons which is less than 1, hence this cost function enhibits Economies of scale. 2 . Tes Seanned CamScanner tan