3 In-kind In-kind vs. cash transfer Now we consider a possible policy application. Consider a consumer who consumes two goods: education and money spent on all other goods, with utility function U(21,22) - 112, and budget constraint 50r1 + 1 - 10000. 2.1 Find the utility-maximizing quantities of goods and 22 as a function of a. Suppose the government would like to increase the welfare of this consumer by subsizing education. One proposal is to increase the consumer's income from 10000 to 15000 (for example, by introducing a program like the earned income tax credit). Let's call this policy as cash transfer program. 2.2 State the new budget constraint and calculate the new utility-maximizing quan- tities of goods Z, and Ig. Compare your answers to those of 2.1. Now, consider an alternative program that simply gives the consumer 100 units of good 1 (for example, the Pell grunt program that provides grants that can be spent only on education). Let's call this as the in-Kind transfer program. You might have noticed that the two programs have the same cost. 2.3 Illustrate the consumer's budget constrant in this case. Note that the constraint is not linear anymore. 2.4 Now, let's consider some cases involving different values of a. First, let - 1. Show that the optimal value of under the cash transfer is more than 100 Explain why, in this case, the consumer is equally well-off under the cash transfer and in-kind transfer program. 2.5 Show that the amount of 1, consumed under the cash transfer program is in creasing in a. Find a value a' such that the optimal valize of I, under the cash transfer program is 100. Explain why the consumer whose value of a is above a' is equally well-off under the cash transfer and in-kind transfer program. 2.6 Consider a consumer for whom a