e refer to the questions given.

Suppose y t =6k t 0.5 (the per worker production function), d=0.1, n=0.02, and the aggregate savings function is given by S t =0.3Y (the savings rate is 0.3).

1) Solve for the steady state level of capital per worker (k), the steady state level of output per worker (y), the steady state level of consumption per worker (c), the steady state level of investment per worker, and the steady state level of savings per worker.

2) Suppose that the savings rate falls. What will be the impact on the steady state values of k, y, and c? Use a diagram to illustrate the fall in the savings rate and then state the impact on k, y, and c. (Label everything: including all axes and all curves)

3) Continue with question 2. Provide an discussion of the impact of the FALL in savings rate on the economy; elaborate on what is the economic reasoning for the changes, especially changes in k, y, and c.

4) Use the information above to calculate the maximum consumption per worker possible at steady state and the capital-per-worker that yields this maximum steady state consumption (c_max).

Total Economic Surplus.

A hot dog cart can sell the Astro special to consumers downtown who have a $10 reservation price or sell outside the World Series to game goers who have a reservation price of $20. An equal number of hot dogs can be sold at each site with the marginal and average costs are $6 at each site.

How can the total economic surplus be maximized?

(a) sell only downtown for $10

(b) charge $10 at both locations and go back and forth

(c) go back and forth and price discriminate

(d) sell only at the World Series for $20

(4) Consider the classic game of "Rock-Papcr-SciSSor Therc are two players and each chooses to form their hand in the shape of a rock, a piece of paper, or a scissor. The rules of the game are that "rock beats scissors", "scissors beats paper", but "paper beats rock'". Let the payoff to winning be a > O and the payoff to losing be 0. For simplicity, suppose it is played as a one-shot ganme (no repitition), and that if the two players choose the same straetegy, each receives (a) Depict this 2 player 3x3 normal-form game in a matrix. (b) Solve for the Nash Equilibrium.

Generally, we observe that the demand curve is downward sloping and that the price is inversely related to demand. In this example, as the price rises from $20 to $25, the quantity demanded will become less than 4000 units according to the law of demand to this extent there are less sales. This phenomenon can be explained by a number of facts.

Substitution effect- as the price of a product Increases, the substitutes of this product become relatively cheaper. Consumers tend to prefer cheaper commodity over the costlier one. This will lead to shift in the consumption pattern towards its substitutes hence decreasing it's demand. Then, as the price increases quantity demanded falls.

Number of uses of the commodity- some of the products can be put to multiple uses. Amongst the uses, some are more important while others are less important. When the price of the product goes higher, the consumers will purchase such goods only for more important uses and will withdraw its usage from less important ones. The demand can also fall in such a way resulting from an increase in price.

Direct proof:

Electricity can be put to multiple uses such as cooking, lighting, heating etc. The most important is lighting. When the price of electricity is lower, say $20 consumers will tend to use it for less important purposes such as cooking and heating. However, as the price goes up say up to $25, it will be be used most on more important uses ultimately leading to a fall in demand. Same is the case with other goods.

However, it is also true that the demand curve may not always show the same behavior. Sometimes, it may change in the direction of the change in price. Nevertheless, these are exceptional cases and the law of demand holds good in most of the cases.