# ECON 104 Homework Problems Solution

Consider the following modeli) C = 1500 + mpc (Y – tY)ii) I = 800iii) G = 500iv) X – M = 500 – mpi (Y)where:t = the (flat) tax ratempc = the marginal propensity to consumempi = the marginal propensity to importsuppose mpc = .80, t = .25, mpi = .2Given the information above, solve for the equilibrium output:A) Y* = 3300B) Y* = 5500C) Y* = 1500D) Y* = 18002.We know that the formula for the (government) spending multiplier is 1/(1-mpc(1-t) + mpi). The value ofthe government spending multiplier in this problem is: Round to 2 decimal places.A) 1.33B) 2.55C) 3.33D) 1.673.When we discussed the multiplier we discussed the impact effect. For example, suppose that G increases by100 to 600 and we assume, as we often do, that firms match the increase in demand by increasing Y by 100.In round two, this is an increase in income of 100 to consumers. We will trace out exactly where this100 increase in income goes in the second round. Recall, there are three leakages to address (via taxes,imports and savings).Given that t=.25, we know that .25 of every dollar increase in gross income is a leakage due to taxes. Sincethe increase in income is \$100, we know the leakage due to taxes is:A) \$25B) \$100C) \$75D) 25 cents4.Given that mpi=.2, we know that .2 of every dollar increase in gross income is a leakage due to imports.Since the increase in income is \$100, we know the leakage due to imports is:A) \$100B) \$80C) \$20D) 20 cents5.Given that the MPC=.8, we know that .2 of every dollar increase in gross income is saved. Since theincrease in income is \$100, we know the leakage due to savings is:A) \$100B) \$80C) \$20D) 20 cents6.To find out how much consumption increases we need to take the increase in income (\$100) and subtractout the leakages. So take the \$100 and subtract your answers from #3, #4 and #5 above. When incomeincreases by \$100, consumption increases by:A) \$100B) \$25C) \$20D) \$357.What would happen to the multiplier if the mpi rises to .25? Round to 2 decimal places.A) the new multiplier is 1.54B) the new multiplier is 1.89C) the new multiplier is .65D) the new multiplier is .378.What would happen to the size of the leakage if the mpi rises to .25?A) this would reduce the size of the leakageB) this would increase the size of the leakage9.In this question, we are going dig deeper into the Taylor Rule and it variants (modifications).Federal Reserve data from October 1, 2011:Potential GDP growth y* = 1.7%Actual GDP Growth yA = 2.0%Inflation PCE (actual inflation) A = 2.6%Effective Federal funds Rate = .07%As Taylor assumed, we assume the equilibrium real rate of interest r* = 2% and the optimal inflationrate, the target inflation rate * is also equal to 2%.The standard (original) Taylor rule formula:iff TR = r* + A + 0.5[ A – *] + 0.5 [ yA – y*]Using the ‘standard’ Taylor rule from above and using the data provided, what is the federal funds rateimplied by the ‘standard’ Taylor Rule?A) 2.04%B) 1.56%C) 3.33%D) 5.05%10.According to the actual federal funds rate (use the Effective Federal Funds Rate provided above for 201110-01), is the Fed being hawkish or dovish?A) hawkishB) dovish11.Now consider the modified version of the Taylor using the unemployment gap instead of the GDP gap justlike we did in the lectures. Also, we will use the PCE core rate of inflation instead of overall inflation likeyou used above – the Fed arguably cares more about core inflation than overall inflation.Modified Taylor Rule formula:iff TR = r* + A + 0.5[ A – *] + (-1.25) [URA – NAIRU]Additional needed data from Federal Reserve data from October 1, 2011:Unemployment Rate URA = 8.7%NAIRU = 5.5%Inflation PCE Core (actual inflation) A = 1.8%Now what is the federal funds rate implied by the modified Taylor Rule above?A) -.45B) -.30C) 0.45D) 0.3012.According to the actual federal funds rate, is the Fed being hawkish or dovish?A) hawkishB) dovish