4 The government budget constraint is satisfied therefore G T The taxes paid by

4 the government budget constraint is satisfied

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4. The government budget constraint is satisfied, therefore G = T. The taxes paid by the consumer are equal to the exogenous quantity of government spending.
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Income – Expenditure Identity In competitive equilibrium, the income expenditure identity is satisfied, so that Y = C + G. In this economy, there is no investment expenditure, as the economy is closed. Therefore I = 0 and NX = 0 . The Production Function and the Production Possibility Frontier In this figure, a shows the equilibrium relationship between the quantity of leisure consumed by the representative consumer and aggregate output. The relationship in b is the mirror image of the production function in a. In c, we show the production possibility frontier (PPF), which is the technological relationship between C and I, determined by shifting the relationship on b down the amount of G. The shaded region in c represents the consumption bundles that are technologically feasible to produce in this economy. Competitive Equilibrium This figure brings together the representative consumer’s preferences and the representative firm’s production technology to determine a competitive equilibrium. Point J represents the equilibrium consumption bundle. ADB is the budget constraint faced by the consumer in equilibrium, with the slope of AD equal to minus the real wage and the distance DB equal to dividend minus taxes. In this figure, the PPF is given by the curve HF. From the relationship between the production function and the PPF we can determine the production point on the PPF chosen by the firm, given the equilibrium real wage rate w . The representative firm chooses the labour input to maximise profits in equilibrium by setting MP N = w , and so in equilibrium minus the slope of the PPF must be equal to w, because MRT l,c = MP N = w in equilibrium. Therefore, if w is an equilibrium real wage rate, we can draw line AD that has a slope –w and that is tangent to the PPF at point J, where MP N = w. Then the firm chooses labour demand equal to h – l* and
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produces Y* = zF(K,h-l), from the production function. Maximised profits for the firm are * = zF(K, h – l*) –w(h – l) (total revenue minus the cost of hiring labour), or the distance DH . Now DB is equal to π * - G = π * - T , from the government constraint G = T . ADB is the budget constraint that the consumer faces in equilibrium, because the slope of AD is –w and the length of DB is the consumer’s dividend income minus taxes. Because J represents the competitive equilibrium production point , where C* is the quantity of consumption goods produced by the firm and h – l* is the quantity of labour hired by the firm, it must be the case that that C* is also the quantity of consumption goods that the representative consumer desires and that l* is the quantity of leisure the consumer desires.
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