1. Consumer Behavior & Market Demand

a. In the past, Ani received a university scholarship of Rp2,000,000 per month to purchase textbooks (B) and daily needs (L). At that time, Ani maximized her utility by spending Rp500,000 for textbooks and Rp 1,500,000 for daily needs,

i. Graphically show the allocation of the scholarship that maximized Ani's utility (B on the horizontal axis and L on the vertical axis). (5 points)

ii. Recently the scholarship committee changed the policy regarding the scholarship's fund

allocation. The new policy stipulates:

The total amount of allocated scholarship remains Rp 2,000,000/month

A lump-sum payment of Rp 1.000.000 will be made to the scholarship recipient.This portion of scholarship can be spent for any purposes, either for purchasing daily needs or textbooks.

The remaining Rp 1.000.000 is allocated for purchasing textbooks only, and will be

paid upon submission of a textbook purchase receipt. This means that if the textbook cost less than Rp1,000,000, Ani will merely receive as much as what is written in the receipt. On the other hand, if the textbook cost more than Rp1,000,000, Ani has to cover the remaining cost by using the lump-sum portion of the scholarship.

Using a graph, show the change in budget constraint caused by the new policy, and also the new budget allocation that maximizes Ani's utility. Compare the level of utility before and after the policy change in your graph.

b.The utility function of an individual for food (M) and clothing (P) is represented by (, ) = . If the price of food is _m = Rp 20,000 per unit and the price of clothing is _p = 100,000 per unit:

i. How many M will be given up to get 1 additional unit of P (MRS) when utility is maximized?

ii. At the moment, the individual is not maximizing her utility and uses her income to consume more M and less P than her utility maximizing bundle. Compare the MRS of this level of consumption with your answer in part (i) - is it larger or smaller? [Hint: sketch the two points consumption bundles to help you answer this question].

2. Production Technology and Cost

Your friend, a FASILKOM UI alumni, wants to start a business in apps development, because during pandemic time many start-ups need apps development services for their business. He, therefore, looks for programmer (labor-L) and cloud server (capital-K) to start producing apps. He plans to hire jobless fellow alumni, and estimates that the salary for a programmer is Rp 4,000,000 per week. The rental cost of a cloud server is Rp 1,000,000 per week. Currently, your friend has already rented 4 cloud servers. To develop an app, the production function consist of equal proportion of programmer and cloud server, given by = ^0,5 + ^0,5.

a. Calculate the following:

i. In the short term, if your friend has Rp 200,000,000 per week, how many apps is he able to produce?

ii. If your friend wants to produce 18 apps per week in the long term, how many programmers (L) dan cloud servers (K) are needed, and what is the total cost?

b. Identify mathematically whether your friend's apps business is increasing, constant, or decreasing returns to scale? If your friend asks you (as an economist) for advice, explain the economic interpretation on the characteristic of your friend's app business in the context of returns to scale!

c. "Sunk cost is a fixed cost, but not in the long term." Is this statement true or false? Explain!