# Consider the following model of the economy:C = 50 + 0.6(Y-T)I= 10+0.

Consider the following model of the economy:C = 50 + 0.6(Y-T)I= 10+0.1Y-iG = 100X= M= 0where C is consumption, Y is income, T is taxes, I is investment, i is the interest rate (measured in percentage points, i.e. an interest rate of five percent is i=5 instead of i=0.05), G is government spending, X is exports and M is imports.1. State the equilibrium condition for GNP (national income) and give a brief explanation of what it means. Solve for national income as a function of the unknown variables, i and T.2. Now assume that the government budget is balanced, and write income as a function of the interest rate. Plot this curve in i-Y space. State and interpret the slope of this curve.3.Assumethat i=10. What is the value of autonomous spending? What is the value of the multiplier? Interpret the multiplier.4. The government decides to increase spending by 10. If it doesnÂít raise taxes, what will the new values of autonomous spending, the multiplier, and equilibrium income be? Give a brief explanation of why income changed by as much or as little as it did. If the government raises taxes at the same time to maintain a balanced budget, what will the new values of autonomous spending, the multiplier, and equilibrium income be? Give a brief explanation of why income changed by as much or as little as it did.5. Now, instead of assuming that the government collects a fixed amount of taxes, assume that it collects a fixed percentage of national income: T=tY. Assuming the tax rate, t, is one-third, solve for equilibrium income, autonomous spending, and the multiplier. Explain any differences with your answers to part 2. Is the government budget balanced? What happens now if the government increases spending by 10? State and briefly explain the changes in equilibrium income and the government budget deficit.