G 1 a c b g 2 eg p 2 ac ab p 1 cb ab e xample m74 you

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G 1 A C B G 2 EG p 2 = AC AB p 1 = CB AB E XAMPLE M.7.4: You are going into a risky venture, which has two possible outcomes, 1 or 2. The venture will pay you $70 if outcome 1 occurs or $130 if outcome 2 occurs. (a) If the probability of outcome 1 is 60%, what is your expected gain? (b) If your expected gain is $105, what is the probability of outcome 1? (c) If the gain from outcome 1 is still $70, the probability of outcome 2 is 0.3, and your expected gain is $100, what is now the gain if outcome 2 occurs? Answer : The basic relation for answering all three questions is Expected Gain (EG) = p 1 G 1 + p 2 G 2 , (M.7.1) where p 1 and p 2 are the probabilities that outcomes 1 and 2, respectively, will occur, G 1 and G 2 are the gains if each occurs, and p 1 + p 2 = 1. In Figure M.7-2, p 1 = CB/AB , p 2 = AC/AB , and p 1 + p 2 = ( CB + AC ) /AB = 1. If p 1 = 1.0 (and hence p 2 = 0), then CB = AB, and C = A. If p 1 = 0 (and hence p 2 = 1), then CB/AB = 0, and C = B. (a) EG = 0.6(70) + (1 – 0.6)(130) = 42 + 52 = $94. (b) EG = 105 = 70 p 1 + 130(1 – p 1 ) = 130 – 60 p 1 , and so p 1 = (130 – 105)/60 = 5/12. (c) EG = 100 = (1 – 0.3)(70) + (0.3) G 2 , and so G 2 = (100 – 49)/(0.3) = $170. FIGURE M.7-2
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2. Exercises 1. At Store A, 40% of the goods are priced at an average price of $12/unit. The average price for all goods is $24/unit. What is the average price of the other 60% of the goods? 2. At Store B, 60% of the goods are priced at an average price of $12/unit. The average price for all goods is $24/unit. What is the average price of the other 40% of the goods? 3. Marvellous Moe’s Discount Emporium has a special “We pay the GST!!!” event. You buy an item with no other sales tax on it and a ticket price of $20.00, and sure enough, you pay only $20.00. If the GST is 7%, how much GST have they paid on your behalf? 4. In Chapter 2 of the text, it is shown that it is immaterial whether a unit sales tax is collected from buyers or sellers: the end result will be the same in either case. Is the same true when there is an ad valorem (or percentage) sales tax? Suppose that the demand curve in a market is given by P B = 120 – 1.5 Q and the supply curve by P S = 20 + Q , with P in $/tonne and Q in tonnes. (a) Calculate the initial equilibrium price and quantity exchanged. (b) Suppose that an ad valorem sales tax equal to 50% of the sellers’ price is imposed on sellers. Give the formula for the “tax-ridden” supply curve facing buyers, and calculate the new equilibrium. (c) Suppose that an ad valorem sales tax equal to 50% of the sellers’ price is imposed on buyers. Give the formula for the “tax-ridden” demand curve facing sellers, and calculate the new equilibrium.
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