Question

A hypothetical economy produces two goods: Capital goods and Consumer good. Provide its resource limit, the economy is able to produce any of the following combinations of capital ad consumer goods.

Capital Goods	Consumer goods
500 400 300 200 100 0	0 900 1600 2100 2400 2500

1. Using the data above, graph the PPC
2. Comment on the nature of opportunity cost (i.e. Increasing, decreasing, or a constant opportunity cost?)
3. Depict the inefficient, unattainable and efficient points of production for this economy.
4. What is the opportunity cost of producing 500 units of capital goods?
5. Consider the economy’s production possibility capacity for the combinations of capital goods (K) and Consumer goods ( C) is given by: C=10-X³/4. Give this, draw the Production Possibility Frontier for this economy and identify if the economy is operating an increasing, decreasing or constant opportunity cost. Support your argument with proof

Answer 1

(a) PPC is the combination of all level of commodity consuming while utility level is same at all points.

(b) Opportunity cost is what you sacrifice/what you gain. As the favorable good is not given of the consumer you have to assume two cases where the consumer sacrifies capital goods for consumer goods and the second case in which consumer sacrifies consumer goods for capital goods.

First case

he sacrifice 100 units and gain 900 units. MPC is 100 / 900

sacrifice 100 and gain 700, so MPC is 100 / 700

sacrifice 100 and gained 500, so MPC 100 / 500

sacrifice 100 and gain 300, so MPC is 100 / 300

sacrifice 100 and gained 100 so MPC is 100 / 100

here you can see that MPC is rising

Second case

sacrifice 900 to gain 100, MPC = 900/100

sacrifice 700 to gain 100, MPC 700 / 100

sacrifice 500 to gain 100, MPC = 500 / 100

sacrifice 300 to gain 100, MPC = 300 / 100

sacrifice 100 to gain 100, MPC = 100 / 100

Thus MPC is falling here.

If we have the condition given that consumer likes one good over another, we would have taken only one case.

(c) Points that lies outside the PPC curve is unattainable points, points lies on the boundary are efficient level and points lies within the boundary are attainable points.

(d) At 400 units of capital goods they were producing 900 units of consumer goods. Thus to produce 500 units of capital goods they need to let go off 900 units of consumer goods. So MPC = 900 / 100 = 9

(e) The equation is not complete as the there were two goods produced K and C and the equation holds relation between C and X, even if i assume X to be K is it X to the power 3 or X multiplied with 3