In this question we will adjust the is-lm curve seen in class slightly. in particular, we will assume that taxes are taken as a percentage of income rather than as a lump sum. then we have c = a + b(1 − τ )y where τ is the percentage (between 0 and 1) of income the government collects in taxes (so that 1 − τ is left to the consumer). assume that investment is a linear function of the interest rate i = e − fr and government spending is fixed at g = g¯ a. derive the is curve (solve for r as a function of y and parameters) b. which parameters affect the slope of the is curve and which affect the intercept? now let: a = 500, b = 0.8, τ = 0.25, e = 5000, f = 300, g¯ = 2500 c. what is the is curve with these numbers? d. what is output if the interest rate is 10%? what if it is 5%? 15%? assume money demand is given by: md p = 2y − 1000r and that the price level is fixed at p = 1 and the money supply at ms = 10, 000 4 e. what is the lm curve with these numbers? f. using the is curve in part c and the lm curve in part e, find the equilibrium interest rate and output for this economy. g. how much does the government collect in taxes in equilibrium? what would the new equilibrium income if the government eliminated the income tax and instead collected a lump sum to get the same total tax revenue? h. government spending increases by 500. compare the increase in income in the model with the income tax to the model with the lump sum tax. explain the economic intuition.