ECON 2123 Problem Set 1 Solution

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1 ECON 223 Problem Set Solution Instructor: Prof. Wenwen Zhang TA: Mr. Ding Dong Due at 5:00 on Monday, March 5th, 208 Question : Suppose that a very simple economy produces three goods and service: Pizzas, Haircuts, and Backpacks. Suppose the quantities produced and their corresponding prices for 2002 and 2006 are showed in the table below: (a). What is nominal GDP in 2002 and in 2006? (b). Taking 2002 as the base year, what is real GDP in 2002 and in 2006? (c). Taking 2006 as the base year, what is real GDP in 2002 and in 2006? (a). Nominal GDP of 2002 = 00*0+50*5+200*40 = $9750; Nominal GDP of 2006 = 20*2+45*20+20*45 = $790. (b). Real GDP of 2002 (base year 2002) = 00*0+50*5+200*40 = $9750; Real GDP of 2006 (base year 2002) = 20*0+ 45*5+20*40= $0275. (c). Real GDP of 2002 (base year 2006)= 00*2+ 50* *45= $200; Real GDP for 2006 (base year 2006)= 20x2+ 45x20+ 20x45= $790. Question 2: During a given year, the following activities occur: i. A silver mining company pays its workers $200,000 to mine 75 pounds of silver. The silver is then sold to a jewelry manufacturer for $300,000. ii. The jewelry manufacturer pays its workers $250,000 to make silver necklaces, which the manufacturer sells directly to consumers for

2 $,000,000. (a). Using the production-of-final-goods approach, what is GDP in this economy? (b). What is the value added at each stage of production? Using the value-added approach, what is GDP? (c). What are the total wages and profits earned? Using the income approach, what is GDP? (a). Only silver necklaces are final goods, thus GDP= value of silver necklaces = $,000,000. (b). At stage one: No intermediate goods. Value added = value of silver = $300,000; At stage two: Silver is intermediate goods. Value added = value of silver necklaces - value of silver = $,000,000 -$300,000 = $700,000. The GDP (using approach of value-added) = $300,000+$700,000 =$,000,000. (c). At stage one: Wage for workers = $200,000; Income of silver company owner = $300,000-$200,000 = $00,000. Total wage and income = $300,000; At stage two: Wage for workers = $250,000; Income of jewelry manufacturer = $,000,000 - $300,000- $250,000 = $450,000. Total wage and income =$700,000. The GDP (using approach of total income) = $300,000+$700,000 =$,000,000. Question 3. Suppose that the economy is characterized by the following behavioral equations: C = Y D I = 50 G = 50 T = 00 Solve for the following variables: (a). Equilibrium GDP (Y) (b). Disposable income (Y D ) (c). Consumption spending (C) 2

3 (a). Aggregate Demand Z = C + I + G = (Y T ) At equilibrium, total production = aggregate demand: Y= Z; Or equivalently,y = (Y 00) Y = 000 Thus, Equilibrium output is 000. (b). Y D = Y T = = 900. (c). C = Y D = = 700. Question 4. Balanced budget multiplier Suppose that the economy starts with a balanced budget: G = T. If the increase in G is equal to the increase in T, then the budget remains in balance. (a). Solve for equilibrium output. (b). By how much does Y increase when G increases by one unit? (c). By how much does Y decrease when T increases by one unit? (d). How does the specific value of the propensity to consume, c, affect your answer to part a? Explain. (a). Y = C + I + G Y = c 0 + c (Y T ) + Ī + G Y = c 0 + c Y c T + Ī + G ( c )Y = c 0 + Ī c T + G Y = ( c ) [c 0 + Ī c T + G] With the assumption that G=T, above equilibrium condition can be written as: () Y = [c ( c ) 0 + Ī + ( c )G] (if you replace T with G); Or (2) Y = [c ( c ) 0 + Ī + ( c )T ] (if you replace G with T). (b). From equation () in (a)., Y = [c ( c ) 0 + Ī] + G. Thus, a one-unit increase in G will lead to unit increase in Y. (c). From equation (2) in (a)., Y = [c ( c ) 0 + Ī] + T. Thus, a one-unit increase in 3

4 T will lead to unit increase in Y. (d). From Y = ( c ) [c 0 + Ī + ( c )G], it can be seen that, given autonomous spending level, a higher c leads to a higher equilibrium output, Y. Question 5. Automatic stabilizers In this chapter we have assumed that the fiscal policy variables G and T are independent of the level of income. In the real world, however, this is not the case. Taxes typically depend on the level of income and so tend to be higher when income is higher. In this problem, we examine how this automatic response of taxes can help reduce the impact of changes in autonomous spending on output. Consider the following behavioral equations: C = c 0 + c Y D T = t 0 + t Y Y D = Y T G and I are both exogenous. Assume c and t are between 0 and. (a). Solve for equilibrium output. (b). What is the multiplier? Does the economy respond more to changes in autonomous spending when t is larger? Explain. (c). Why is fiscal policy in this case called an automatic stabilizer? (a).y = C + I + G Y = c 0 + c (Y T ) + I + G Y = c 0 + c (Y t 0 t Y ) + I + G Y = c +c t [c 0 c t 0 + I + G] (b). The multiplier is c +c t. When t is larger, the multiplier c +c t is smaller, thus at any given level of autonomous spending [c 0 c t 0 + I + G], the equilibrium output will be smaller. Or equivalently speaking, given any positive change in autonomous spending, the increase in output tends to be lessen when t is larger, so does Y D and C. In other words, the economy responds less to changes in autonomous 4

5 spending when t is larger. (c). Compared with the multiplier in standard goods market model of chapter 3: c, in this question the multiplier is c +c t. Because of the automatic effect of taxes on the economy, the economy responds less to changes in autonomous spending than in the case where taxes are independent of income (since c +c t < c ). As output tends to vary less (to be more stable), fiscal policy is called an automatic stabilizer. Question 6. Suppose that a persons wealth is $50,000 and that her yearly income is $60,000. Also suppose that her money demand function is given by: M d = $Y (0.35 i) (a). Derive the demand for bonds. Suppose the interest rate increases by 0 percentage points. What is the effect on her demand for bonds? (b). What are the effects of an increase in wealth on her demand for money and her demand for bonds? Explain. (c). What are the effects of an increase in income on her demand for money and her demand for bonds? Explain. (a). B D = 50, , 000(0.35 i) If the interest rate increases by 0 percentage points, bond demand increases by $6,000. (b). An increase in wealth increases bond demand, but has no effect on money demand. Because money demand depends on income (a proxy for transactions demand) rather than wealth. (c). An increase in income increases money demand, but decreases bond demand. Because at any given level of wealth, an increase in money demand implies a decrease in bond demand. Question 7. The Money Multiplier (Modified) 5

6 Assume the following: i. The public holds no currency. ii. The ratio of reserves to deposits is 0.. iii. The demand for money is given by: M d = $Y (0.8 4i) Initially, the monetary base is $00 billion, and nominal income is $5 trillion. (a). What is the demand for central bank money? (b). Find the equilibrium interest rate by setting the demand for central bank money equal to the supply of central bank money. (c). Given that overall money supply equals (/reserve ratio)*monetary base, is it equal to the overall demand for money at the interest rate you found in part (b)? (d). What is the impact on the interest rate if central bank money is increased to $300 billion? (e). If the overall money supply increases to $3,000 billion, what will be the impact on i? [Hint: Use what you discovered in part (c).] (a). All money is in checking accounts, so demand for central bank money equals demand for reserves. Therefore, demand for central bank money = 0.($Y)(.8-4i). (b). b. $00B = 0.($5,000B)(.8-4i) i = 5%. (c). Money multiplier = /reserve ratio = /.=0. M s = 0* $00B=$,000B M = M d at the interest derived in part (b). (d). If H increases to $300B the interest rate falls to 5 %. (e). The interest rate falls to 5%, since when H equals $300B, M = 0*$300B = $3,000B. THIS IS THE END OF PROBLEM SET Solution. 6