Question

Section 7 (Function Arithmetic and Conposition) Math 111, Spring '19, Frice 6. The famous economist John Maynard Keynes originally proposed the notion of function, a measure of how much an individual will consume (spend on goods and services) as a function of his or her income. He suggested that it propensity to consume and vertical axis intercept called the individual's autonomous spending. For a particular factory worker, his marginal propensity to consume is 0.55 and has $38, 000 per year in autonoimous spending. The factory worker's income is expected to be modeled by I(t) = thousand dollars, t years from now. consumption as linear with the slope called the marginal 1090t t + 1 a) Find a formula for C(I), the consumption function (in thousands of dollars) for the factory worker having annual income I thousand dollars. b) Write a formula for the factory worker's consumption as a function of time, t years from now. (c) How much does the model predict the worker will be consuming in 2 years? (d) What does the model predict for the factory worker's annual consumption in the long run? LO

Answer 1

(a) Pind a formula for C(n, the consumption function (in thousands of dollars) for the facjory worker having annual income I thousand dollars. Tha cannapi famck c(i) D'38,UD F0.SSx nl prperaiy tautongmouo spining =38 houran (b) Write a formula for the factory worker's consumption as & function of time. t vears frem is 40+ 9ot I(4+9t 2 (t+) - S.S { 4-+9t) 38500 (ヒ+リ (e) How much does the model predict the worker will be consuming in years? For t2ye, harr C L2) 11 49 2) +38 1 2+9) +38 2 (21 121t4 235 thomrndo 78 thowndo $78,333.33 (d) What does the model predict for the factory worker's annual consumption in the long run? Pre dictevlw in un 4+9t) +38 im 2 (t + ) +38 Lim 2 Yt (2 +0) +38 49.5 8 87.s hswondo - 37, soD