Question

Question 1 (1 point)

Suppose the consumer's utility function is given by

U(x1,x2)=x1^ax2^b

, where a=7.0, and b=4.0. Suppose further, the price of good 1 is 2.6, price of good 2 is 0.5 and income is 43

Finally suppose the price of good 1 has decreased to 0.4

What is the substitution effect for good 1 and good 2? Round your answer to two decimal places

Suppose the consumer's utility function is given by

U(x1,x2)=x1^ax2^b

, where a=2.0, and b=5.5. Suppose further, the price of good 1 is 1.4, price of good 2 is 2.7 and income is 94

Finally suppose the price of good 1 has decreased to 0.4

What is the income effect for good 1 and good 2 Round your answer to two decimal places

Answer 1

Here the consumer utility fr. is. (x, Rr) - su ab where az 7.0 and b=4.0. Alo Given price of good 1 (b) = 2.6 price of good 2 (12) = 0.5 Income (m) = 43. so the ordinasy demand curve of good 1 (xi) and godda (ur) are. R ate atb 43 t one Hy 2.6 – 10.52 ho - 301 28.6 2016 - 10.52 At my att 201 43 54.73 0.5 Now In the px, equation of the budget Line. & Pada – us.

As p. = 2.6 $2=0. 5 m = 43. 2.6 x + 0.5 X2 = 43. when &q=0. 2.6% = 43 x =43 = 16.54 26 when Noo 0.5 X2=43 d2 = 43 - 86 Os Refer to the figure. 63.14 5473 V 40.18 10.52 16.54 50.225 +8.9 x, x = 10.52 here and the H= optimal bundle 54.73

Now the price of good I decreases to 0.4 but the income remain the same so the real income of the consumer increases. So to find the substitution effect for geod & the consumer have to compensate so that to purchase the old bundle. So now the income after compensating in is. pix, & bz X2 = m. 1 where his new price and wis new income . p =0.4 P2 = 0.5210 ULO be have. x= 10.52 - 54.73 2x + P222 = wis dust knitto, est un 0.4 (10.52) + 0.5 (54.73) - u - 4.208 + 27.365 - 31.57 So w = 31.57

Now the equation of budget line is alle b, x, it ba az a As p = 0.4 p 2 = 0.5 = 31.57 so 0.484 t o. 582= 31.57 eur of the consumer purchase only good I. 00.48= 31.57 x= 31.57 - 78.93 0.4 of the consumer purchase only good 2. 0.5 x = 31.5td o o x2 = 31.57 = 63.14 0.5 o after compensating Now the we get x = a optimal bundle ) -2012 ath 12.12 =73157 31.57 2.10 7th 6.49 busest o n 7 31.5t 9.57 04 - 50.225 ath 02 31:57 764 6.5

3.7 = 220.99 0.5 5.5 - 40.18 good I falls. So Previously optimal bundle for was 10.52 but as price of good i optimal bundle is 50.225.. good I consumption increase by 56.225 – 10.52 = 39.705 unit Previously good? optimal bundle was. 54.73 unit and now as price of good 1 falls good a consumption, falls to 40.18 So good a consumption falls by 54.73 – 40. 18 a 14.55 unit This is shown in the figure above.