Question

Closed Economy In the Short Run. I have solved (a) but confused on how to solve the rest.

I-MPC sider the following model of a closed economy in the short run Total demand is given by the accounting identity I MPC Y =C+I+G The consumption function is C = ao + a (Y +TT - TT) - MPC The tax schedule is Tx = To + TY Transfers are given by Th = Tro – hY Investment demand is I=bo-bzi where Y is production, C private consumption, I investments, G government consump- tion, Tx taxes, Tr transfers from the government to households, i the interest rate, and ao, 01, bo, bi, To, T, Tro, and h are constant parameters. government consumption is initially G = 60, and the parameter values are: ao = 15, aj = 0.75, bo = 40, bi = 400, To = 20, T = 0.3, Tro = 60, and h = 0.2. Assume that the central bank keeps the interest rate constant at i = 0.05. 1 - 60 Solve the model for equilibrium production (Y). Calculate the effects on production Y from increases in government consumption G and lump-sum taxes To. () What is equilibrium production (Y)? (b)) What is the multiplier for government consumption (AY/AG)? (C) What is the multiplier for lump-sum taxes (AY/AT.)? ((d) Assume that the government increases government consumption by AG = 12. Suppose that production was initially on the natural level, and that the central bank, instead of keeping the interest rate constant, adjusts the interest rate (i) to keep production on the natural level (to avoid overheating of the economy). By how much (Ai) will the central bank raise the interest rate?

Answer 1

a) Aggregate demandi Y:C+I+G = 20+ air + Tv -T2) + bo-6,1 *.GI = 20 **1 [Y+ Tro-hy-To-99)+60-brit Get = ao+al (tro-to + (1--r)] + bo-blito P = 20+ a1(Tro-To) + a,(i-th-ny) Y + 60-bit Gut [actal (Tro-To) +66+687 +01 (1-6-3) 7-6, : Y = Ā + a, (-h-3) T - bii when Ā = aota (Tro-to)+ bo to wr, [-all-th-3)] Y = Ã -bii Wh .:. y* Ā - bii (9) ( - 6 - 1) Griven; ao=15, bo:40 , 2, = 0.75 , To - 20, T7060 G1=60 : Ā.= 15+ 0.75 (60-20) + 40 + 60 = 145 :.on(i-h-ny) = 0.75 (1-02-0: 3) = 0.375 :. bii = 100(0.05) = 20 :. Y*: 195-30 - 200 og det i-a.co-hugoś25:16 đã đi đến -- -- -- -- 6 -

(d) Natweal rate of output : change in output for G 7 = 200 ay La = 1.6 i AY = 1.6*12 = 19.2 Change in output for i da ne nabi-m-3) =-640 Now to keep y constant ; Diario - 003 AY = - -19.2 -640 = 0.03 Then central bank must raise interest by 0.03; :. si = 0.03. Proof: G = 60+12. = 42 i = 0.05 +0:03 = 0.08 Leist bij: 400(0.08) = 32 * 157 · 32 200 ✓ 0:625 . ..