Suppose the economy's production function is Y = A(300N – N2). The marginal product of labor is MPN = A(300 - 2N). Suppose that A = 10. The supply of labor is NS = 0.05w + 0.005G
(a) If G is 26,000, what are the real wage, employment, and output?
(b) If G rises to 26,400, what are the real wage, employment, and output?
(c) If G falls to 25,600, what are the real wage, employment, and output?
(d) In cases (b) and (c), what is the government purchases multiplier; that is, what is the change in output divided by the change in government purchases?
(a) Setting labor supply equal to labor demand gives N = 0.05 × 10 × (300 - 2N) + 0.005G, which can be simplified to get N = 75 + 0.0025G. With G = 26,000, N = 140. Then w = 10 × [300 - (2 × 140)] = 200 and Y = 10 × [(300 × 140 ) - 1402] = 224,000.
(b) Following the same procedure gives N = 141, w = 180, and Y = 224,190.
(c) N = 139, w = 220, and Y = 223,790.
(d) In part (b), the multiplier is 190/400 = 0.475. In part (c), the multiplier is 210/400 = 0.525.
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