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# Ex4_one_period_model_graph_k.pdf

4 Pages
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Department
Economics
Course Code
ECON 2400
Professor
Wai Ming Ho

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AP/ECON2400A (Fall 2012) W.Ho Example 4: E▯ects of a decrease in K in the one-period closed macroeconomy Consider a one-period, closed economy consisting of a large number of identical con- sumers, a large number of identical ▯rms, and a government. Each economic agent acts as a price taker in perfectly competitive markets. The economic behaviors of the consumers and ▯rms are as described in Example 3. The government’s purchase of the consumption goods is ▯nanced by lump-sum taxes imposed on the consumers, G = T. 1. Draw a diagram with the PPF to illustrate the competitive equilibrium of the economy. Label and describe your diagram. 2. What are the four conditions that a competitive equilibrium must satisfy for this economy? 3. Suppose now that there is a decrease in the capital stock of the economy, K. (a) How does the decrease in K a▯ect the production possibilities frontier? Explain your answer. (b) Show how to determine the new competitive equilibrium of this economy. Illus- trate the income and substitution e▯ects of the decrease in K. (c) Is the new competitive equilibrium real wage higher than that in the original competitive equilibrium? Why or why not? AP/ECON2400A (Fall 2012) W.Ho { Example 4 2 Answers 1. Figure 1 shows the competitive equilibrium of the economy. The competitive equi- librium occurs at point E where the PPF is tangent to an indi▯erence curve. The competitive equilibrium real wage is given by w = MRS E = MRT : E l;c l;c 2. The four conditions that a competitive equilibrium must satisfy are d s (a) The representative consumer chooses C and N to maximize utility, U, taking as given h, w, ▯, and T. The optimal condition is MRS l;c w. d s (b) The representative ▯rm chooses N and Y to maximize real pro▯ts ▯, taking as given w, z and K. The optimal condition is MP = w. N (c) Government budget constraint is satis▯ed: T = G: S d s d (d) Market-clearing: labor market, N = N ; and good market, Y = C + G. 3. (a) The PPF is given by C = zF(K;h ▯ l) ▯ G. A decrease in K shifts the PPF downward proportionally. Holding z and G constant, a decrease in K implies a decrease in output for any given level of labor input. Hence, there will be fewer goods available for consumption, C, for any given level of l. The new PPF is denoted by PPF . 0 (b) The new competitive equilibrium is at point A where the new PPF is tangent to an indi▯erence curve. The total e▯ect (from point E to point A) can be decomposed into two e▯ects: A substitution e▯ect (from point E to point H): as leisure becomes less expensive relative to consumption goods, the economy moves towards fewer consumption and more leisure. An income e▯ect (from point H to point A): as capital input falls and labor input becomes less productive, the income of the economy decreases, and the consumption of both goods and leisure decrease. We can obtain the two e▯ects by shifting the new PPF (PPF ) parallelly upward
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