Question

As in the previous two questions, the Anteater Family can spend its money on education (e) or other goods (g). The family's utility over e and g is given by 0.5 0.5 The Anteaters have income of $100,000 to spend on e and g each year. Now, however, there is the option of sending children to public school. If the Anteaters send their children to public school, they get 1500 units of e for a price of $O. If the Anteaters send their children to private school, they can choose any number of units of e at a price of $20 per unit (as in Question 15). The price of all other goods remains $25 per unit. Calculate the utility level associated with sending their children to public school and spending all their money on other goods. Calculate the utility level associated with sending their children to private school and spending their remaining money on other goods (i.e., the utility level associated with the choice derived in question 16) Given your answers, the Anteaters will send their children to Selectl school In this case, free public educationSelect 1 the quantity of education the I Select ] increases Anteater children receive. does not change

Answer 1

Here, the utility function is given as U(e,g) = e^.5*g^.5.

The income is = $1,00,000.

The Marginal utility for good 'e' = dU/de ( by differentiating the utility function) = 1/2e^-0.5 * p^0.5.

The Marginal utility for good 'g' = dU/dg = 1/2e^0.5g^-0.5.

Now, as per the optimality condition, solving it for private school consumption,

MUe/Pe = MUg/Pg = g/20 = e/25 =g/e = 20/25 = 4/5

g/e = 4/5 ; 5/4g = e.

Now, putting this value of 'e' in the budget constraint,

M = e*Pe + g*Pg ( Pe = price of e, Pg = price of g, M = Income)

1,00,000 = 5/4g*20 + g*25 ( Since, Pe = 20, Pg = 25 given)

1,00,000 = 25g + 25g

1,00,000 = 50g

g = 2000

Therefore, putting the value of g in e = 5/4g, we get, e = 2500.

So, here, e= 2500 and g= 2000.

Now, for public school, for 1500 units of 'e' the price of 'e' is zero.

So, the budget constraint for public school would be,

1,00,000 = e*Pe + g*Pg

1,00,000 = 1500 * 0 + g*25 (Since, Pe = 0 and Pg = 25)

1,00,000 = 0+25g

1,00,000 = 25g

g= 4000

And e = 1500 (given)

Now, by putting the values of 'e' and 'g' of private school in the utility function, we get, U = √e*g √2500*2000 = 2236.06

Doing the same for public school, we get, U = √eg √4000*500 = 774.596.

Therefore, anteaters will send their children to private school as the utility is more there.

Therefore, in this case, free public education decreases the quantity of education the amateur children receive.