Lesson 4
a. In lesson 4 we write the budget constraint as I = XPX + YPY. Write this as a linear equation with Y on the left as in Y = … . What is the slope of this line. Explain this.
Px*X+Py*Y=I
Therefore Py*Y=I- Px*X
Y=I/Py-(Px/PY)*x
This equation has the linear format of y=b+mx,and thus, the slope of the budget line is –(Px/Py) The slope of the Budget Line tells how much of the good on the y axis we must give up to buy one more unit of good on the x axis, SO if we go back to the fish and fruit example the consumer can transform fruit Y into fish X at the rate of Px/Py. Giving up one unit of fish means saving Px dollars with which we can buy Px/Py units of fruit Y.

b. In lesson 4 we discuss the pure income effects on income increases and decreases and of price inflation and deflation. Consider a 5% increase in income accompanied by a proportional 5% increase in prices. How will this affect the budget line, explain?
Change in income: Increase in income result in parallel shift outward of the budget line. The intercepts change, the slope remains the same.
• Change in price: Increase in price of good 1 result in shift of the horizontal intercept of the budget line inward.
• Change in both prices and income by the same factor: Budget set remains the same. Therefore if we increase both income and price by the same factor 5% our budget line will remain the same.

c. If the income expansion line (lesson 4) is a straight line, the income elasticity of demand of both goods is equal to 1. Explain why – prove it.
If the percentage change in quantity demanded is equal to percentage change in income is known as income elasticity of demand equal to one. The following diagram shows this graphically:

If there are n goods on which the consumer spends her budget, how many of them can be inferior? Explain.
If there is tow goods only one can be inferior, but if there is n goods, the number can be n+1 since we must have at least one good that is normal that will have consumption increase with more income otherwise if all goods are decreasing we would eventually get to zero consumption of anything, and would have nothing to do with all that income =)
5. Consider the transition from short run to long equilibrium in the model of perfect competition What if technology were changing rapidly? How would this situation be different?
If technology is changing rapidly, this would create opportunity for all firms to take advantage of this and create super normal profits in the short run, potentially for all who do, since it is available to everyone, however eventually the effect of this technological advancement will wear off and until something else comes along that will once again allow firms to lower costs or increase production profits will normalize in the long-run.
If technology was changing, the variable costs would most likely decrease , improving production efficiencies and decreasing most likely both AC an MC. The quantity produced by each company increases in the short-run. Since all companies increase their quantity produced, market supply increases (shifts right) and the market price falls. However, the decrease in the price is less than the decrease in the Average Total Cost, and economic profits rise. What if producers competed by differentiating their products? How would this situation be different Could the assumptions of perfect competition still be maintained?
Same as in the situation with new technology not available to all producers, these companies would create supernormal profits, as long as no other company can easily imitate their product, therefore increasing the supply and decreasing the prices.
Undifferentiated or homogenous products and perfect information about prices are characteristics that imply the law of one price. That is, transactions between buyers and sellers occur at a single market price. Because the products of all firms are perceived to be identical and the prices of all