Question

1. Marginal productivity of capital in a given economy is described by the following function: MPK = 48/J(K), where K stands for aggregate capital and MPK for marginal productivity of capital. (a) Use words to explain what MPK measures. (b) Calculate MPK when K = 16 and when K = 64. How does MPK change as K increases? What property does this MPK function capture? (c) Write down the two assumptions of the classical environment and explain what they imply. (d) Using a graph, illustrate equilibrium in the capital market under the classical environment assuming the MPK function from above. Label all relevant variables. (e) Again using a graph, illustrate how the equilibrium in (d) changes when TEP(A) decreases. (f) Maintaining the classical environment and the MPK function from above, determine the equilibrium rental rate of capital when K^s = 9.

Answer 1

48 지 48 4 = 12 =6 V64 8 (a) Marginal product of capital CMPW) meascurces the extra amant of production by increasing capital by an additional cit. (b) MPK 48 → When K=16, MPK - V6 when K=64, MP r = 48 48 Therefore, when K increases, mix decreases. © Assumptions Marginal product in creeases at a diminishing reate, which means that the reate of change of mp is negative as observed above & Payments to each of the factors of production based on their respective marginal producte exhaust the total output. The production exhibits constant reetarons to scate. Full employment is also assumed by classical theory. (d) Figure 1 denotes a capital market, where demand for capital and supply of capital are shown by D and s respectively. The equiele brúsem rcate of interest is et and supply of saving equals demand for coresment (e) when TFP increases, demand for investment increases as shown in fig. 2 wherce demand I to D' Equilibrium Rate of interest increases and equilibrium kerel of capital also increases. (f) when K=a. → Equilibrium rental cate = 16 (g) When Ka= ks the situation is called equilibriuos, wheree demand for capital (or investment) equals supping of capital Con earings (h) of both capital and labor intre in a cabo-Daegias production function triples, the output also triples. This preoperty is called constant returns to scale. S a cureve shifts fream D R! 48 MPx = 48 -16 D 3