Answer:
a, The PPF intersect the Y-axis at 1000 units of luxury goods
The PPF intersect the X-axis at 500 units of necessity good
It means that when the society produces zero units of necessity, it can produce 1000 units of luxury goods and if they use all resources to produce necessity, they can produce 500 units only
b. The economy can produce at a point inside the curve IF (1) There is underutilized of the available resources. (2) There is inefficiency in the use of resources
c. I will want to produce more necessity than luxury. The decision on which point the society will want to be depend on the type of economic system being practiced by my society, if it is free market, the price system will determine it and for a socialist system, the government decides.
d. If I am a dictator, I will make decrees as to the economic direction I want for the society and where the product distribution is left to the free market, the price system decides.
Explanation:
The production possibility frontier is a graph that shows the trade-off between two commodities which a country can be assumed to produce. An economy can operate on the PPF in which case it is using its resources to the fullest. It can operate inside the curve which means under-utilization of resources or inefficiency in resources utilization. A country cannot operate outside the curve except there is technological progress or economic growth.
Part a) The Cob Douglas production function is given as:

To show that this function is homogeneous with degree 3, we introduce be a parameter, t.

Using properties of exponents, we on tinder:

This implies that:


Simplify the exponent of t to get;

Hence the function is homogeneous with degree, 3
Part b) To verify Euler's Theorem, we must show that:

Verifying from the left:




Q•E•D
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Answer:
III) Increase its gross margin
Explanation:
If the company increases its gross margin, it will have a direct impact on the company's net profit. The higher a company's net profit, the higher its value = higher stock price.
The only option that increases the value of the company is to increase its net profit, since:
- an increase in inventory will result in a lower stock price
- a decrease in the asset turnover ratio will result in a lower stock price
- the issuing of stock dividends will only increase the price of stock in the short run, later the price will adjust down since the company's book value will lower