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Sports Statistics

Q1: You are attending a championship soccer match with your family. In your pocket only $40 to spend on Popcorns(S) and Cokes (C), supposed to allocate such amount to maximize satisfaction of the two goods, where the price of popcorn is $5 and the price of coke is $4, looking at the table below:
Various levels of S and C MUs MUs/Ps MUc MUc/Pc
1 40 120
2 30 80
3 25 40
4 20 32
5 15 16
6 10 8
MUs = marginal utility of popcorn, Ps = price of popcorn
MUc = marginal utility of coke, Pc = piece of coke

Answer the followings:
1. Fill up the blanks above?
2. Find the combination of popcorns and cokes yields and the level of utility, subject to the budget constraint?
3. Calculate the total utility of the optimal consumption of the two good?
4. What is the marginal rate of substitution(MRS) in such case?
5. State the budget equation in this case?
6. Graph the budget line and an indifferent curve, showing the optimal point?
7. What does the indifferent curve represent? How it relates to the indifference map?
8. What is the level of marginal utility per dollar spent, where you get the maximization or the optimal equation of the two goods?
9. The demand curve is derived from the marginal utility concept, explain?
10. Can you classify this case as a corner solution? Explain?

Q2: Decided on open tailor shop, the following table gives the level of outputs(shirts) produced daily, with the least cost of input combinations (labor wage(w) = $300, and cost of capital, sewing machine(r) = $200) per day:
output Labor # Capital # Long run total cost (LTC) Long run average cost(LAC) Long run marginal cost(LMC)
100 10 7
200 12 8
300 20 10
400 30 15
500 40 22
600 50 30
700 60 42
Answer the followings:
1. Fill up the blanks above?
2. Write down the cost equation?
3. State the total production function?
4. Draw up the graph for LAC and LMC in relation to the output?
5. Graph the Isoquant curve as well as the Isocost curve, with the optimal input combination?
6. In this case, you are operating in competitive market, what are the characteristics of such market?
7. At which price you are supposed to sell the shirt?
8. Draw up the expansion path for outputs and costs in the table above?
9. What is the approximate level of output(varies discretely by 100 units in the table), where profit is maximized and you are economically and technically efficient?
10. What is the Marginal Rate of Technical Substitution (MRTS) in this case?
11. Is the cost structure in the question long-run cost or short-run cost ones, what is the difference between the two, and how can they be related?
12. There are many factors reduce costs, and shift LAC downtrend, identify three of them?
13. At which level of output is the Minimum Efficient Scale(MES)?
14. What kind of demand curve you are facing in this market?
15. Is this competitive market, what is the economic profit, and should it be different in value from the opportunity cost? Explain?

Q3: Abdullah want to expand the capacity of his restaurant, but not sure of the 2020 economic growth (GDP) of the Saudi economy. He has the probability of 40% that the economy will maintain the expected growth rate in 2019 (1.8%) and the probability of 60% it will be little higher (2.1%) as the IMF forecasted. Accordingly, the table below is:
Growth rate 2.1% 1.8%
Probability Dist. 60% 40%
Profit Profit($Million) Profit($Million)
A. Decision maintain capacity 100 persons 3 2
B. Decision expand capacity by 20% 4 1
Answer the following:
1. Compute the expected profits for both decisions?
2. Based on the expected profit only, which decision should Abdullah make?
3. Compute the Standard Deviation for decisions A and B, facing Abdullah?
4. Which decision would Abdullah make, using the coefficient of variation?
5. If Abdullah has no idea of the probability distribution of economic growth, operating in uncertainty world. Using the information above, what decision would Abdullah make, according to each of the following rules:
A. Maximax:
B. Maximin:
C. Minimax Regret:
D. Equal Probability:
6. Which decision is riskier, and how can you classify yourself as risk lover or averter or neutral?