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?
What will be an ideal response?
| (a) | Setting labor supply equal to labor demand gives N = 0.05 × 10 × (300 - 2N) + 0.005G, which |
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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