Question

A. In absence of subsidy what is return to capital in both sectors
B. By how many units of capital does the subsidy increase investment in manufacturing
C. What is the dead weight loss of subsidy

The kingdom of Westeros has two sectors, manufacturing and services. The market for capital is competitive, and capital can move freely between the two sectors. The total amount of capital in Westeros is 120 units 100 -Km, where Km is the number The marginal revenue product of capital in manufacturing is MRPm of units of capital in manufacturing. The marginal revenue product of capital in services is MRPs 80-Ks, where Ks is the number of units of capital in services. King Tommen has decided that the manufacturing sector should be expanded, and therefore grants a subsidy of $10 per unit of capital employed in manufacturing. Thus, individuals who invest in the corporate sector receive $10 in addition to whatever payment they receive for supplying their capital.

Answer 1

Answer (A) : Return to the invested Capital in a sector is defined as the difference between the net income of the sector and the dividends of the sector divided by the total capital of the sector.

  $i.e. Return to Capital =$$\frac{The Net Income - Dividends if any }{The Total Capital}$

Here, the Total capital available is 120 units.

Let us suppose that the total capital units in Westeros is equally distributed between the Manufacturing and the Services Sector, and there are no dividends as of now.

The marginal revenue of the manufacturing sector = 100 – Km

                                                                                            = 100 – 60

                                                                                            = 40

& The marginal revenue of the Services sector       = 80 – Ks

                                                                                            = 80 – 60

                                                                                            = 20

Therefore, the Net income of the manufacturing sector is = 60 x 40

                                                                                                          = $ 2400

& the Net income of the Services sector is = 60 x 20

                                                                                = $ 1200

Therefore, the Return to Capital for the Manufacturing Sector = $\frac{2400 -0 }{60}$

= $\frac{2400 }{60}$

= $40$

& the Return to Capital for the Services Sector =  $\frac{1200 - 0}{40}$

   = $\frac{1200}{40}$

= $30$

Answer (B) :The Subsidy provided by the King is $10 per unit

i.e. for the manufacturing Sector, the total production is 60 units, and the price per unit is $ 40

Now, that the king has given a subsidy of $ 10, it means, that the total subsides given is = 60 x $ 10

                                                                                                                                    = $ 600

If this total increase in the capital due to subsidy is further utilized in the production of further units, then the total increased unit in the manufacturing sector would be:

                                                                                                                = $\frac{Total extra profit}{Actual value of per unit of production}$

= $\frac{600}{40}$

= $15$

Answer (C) : The Dead weight loss of the subsidy given to the manufacturing sector would be if due to the increased price per quantity , the units of capital that are used in services are now diverted to the production of manufacturing sector, in order to earn the profit of subsidy. It has been a trend that when a subsidy is given , the manufacturers focus on earning more and more profit out of the subsidized product and undermine the importance of the other sectors.