Answer Key - Problem Set 3

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2. If f(x) is a linear function of x then it can be mathematical represented in the following form: f(x)=a+b*x, where a (intercept) and b (slope) are two arbitrary constants. Thus, we can represent consumption and saving function with the same analytical expression. For a linear function it is sufficient to know two arbitrary point on the line to find the values of both a and b. For example, took two points form table 6-3 (page 109) in your text: Disposable Income 24000 25000 Consumption Saving First, let find a and b for the consumption function. We know that the slope of the consumption function b is equal to the MPC, thus we can find b by dividing a change in consumption (800) with a change in income (1000): thus our consumption function is: C = 5 000 + 0.8*DI (1) You may use point B to check that it is actually true: A B 24200 25000 b=MPC=ΔC/ΔDI=800/1000=0.8 To find a simply use either point A or B in the following way: since C=a+b*DI, consumption at point A is equal to: C(B) = 5 000 + 0.8*25 000 = 5 000 + 20 000 = 25 000 The same logic applied to the savings function: S=a+b*DI, where b is the slope of the saving function which is equal to the marginal propensity to save (0.2 in this table). To find a for this function use same steps as with consumption function: -200 24 200 = a+0.8*24 000 or a = 24 200 - 0.8*24 000 = 24 200 - 19 200 = 5 000 -200 = a+0.2*24 000 or a = -200 - 0.2*24 000 =- 200 - 4 800 = - 5 000 as a result, the saving function is S = - 5 000 + 0.2*DI (2) Alternatively, you can use your consumption function to derive the savings function: S = DI-C, S = DI - 5000 - 0.8*DI = - 5000 + 0.2*DI 0 i. ii. Using data from the problem 1 fill the following table: Consumption function Saving function intercept a slope b intercept a slope b A-B B-C 300 450 0.95 0.85 -300 -450 0.05 0.15 C-D D-E E-F 750 1000 1300 0.70 0.60 0.50 -750 -1000 -1300 0.30 0.40 0.50 What is the economic meaning of the intercepts a of savings and consumption functions? ANSWER: The value of intercept shows the consumption (savings) when disposable income is equal to zero. That is in case of consumption function a represents the amount household needs to consume in order to survive. - 2 -
05 iii. How will you use equations 1 and 2 to find the break-even disposable income? (You may either show it in a general case or for any given a and b from the table.) ANSWER: To find break even income you have either to equate savings to zero or consumption to disposable income: using savings function: S=0, aS+bS*DI=0 thus DI=-aS/bS using consumption function: C=DI, aC+bC*DI=DI thus DI=aC/(1-bC) for example for the segment A-B aS=-300, bS=0.05, and aC=300, bC=0.95 then S=0 implies that DI=-(-300)/0.05=6000 and C=DI implies that DI=300/(1-0.95)=6000 - 3 -
Page 1: EC132.01(02) Serge Kasyanenko Princ

Answer Key - Problem Set 3

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