Answer to Question #282469 in Macroeconomics for ABEX

Question

9. Consider a production function of an economy:

Y = BKαT βL1-α-β (1)

where Y = output, K = capital stock, T = land, L = labor, B = index

of exogenous technological change, and α and β are elasticities.

(a) Show that growth in output along the balanced growth path is

gY = g + (1 - β¯)n and that growth in output per capita is given

by gy = g - βn ¯ where g = gB/(1 - α), and β¯ = /(1 - α). [Hint:

Assume that land is fixed and exploit the stylized fact that capitaloutput ratio (K/Y ) is constant at steady-state].

(b) What is the long-run growth a function of?

(c) Suppose there is little or no technological advancement in the

economy. What is the fate of the economy with fixed land and a

population growing at a rate of n?

(d) Discuss how the Malthusian checks would operate on this type of

hypothetical economy.

(e) Discuss the implication of this model on economies dependent on

non-renewable natural resources.

(f) How does technology help break the impasse in this model?

Answer 1

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