Yangjie buys smoothies and sushi, The price of a smoothie is 5$ and the price of sushi is 1$ a piece. Each month, Yangjie spends all of her income and buys 10 smoothies and 20 pieces of sushi. Next month the price of a smoothie will fall to 3$ and the price of sushi will rise to 2$ a piece. Assume that Yagjie's preference map is similar to that in Fig. 8.3 (b). Use a graph to answer the following:
1. - Will Yangjie be able to buy 10 smoothies and 20 pieces of sushi next month?
2. - will she want to buy 10 smoothies and 20 pieces of sushi, explain why
3.- which situation does she prefer: smoothies at 5$ each and sushi at 1 $ a piece or smoothies at 3$ each and sushi at 2$ a piece?
4. If she changes the quantity that she buys, which good will she buy more of and which will she buy less
5. When the prices change next month will there be an income effect and a substitution effect at work or just one of them? explain

a) Yangjie can still buy 10 smoothies and 20 pieces of sushi.
When Yangjie buys 10 smoothies at $5 each and 20 pieces of sushi at $1 each,
she spends $70 a month. Now that the price of a smoothie is $3 and the price of
sushi is $2 a piece, 10 smoothies and 20 pieces of sushi will cost $70. So Yangjie
can still buy 10 smoothies and 20 pieces of sushi.
b) Yangjie will not want to buy 10 smoothies and 20 pieces of sushi because the
marginal rate of substitution ...

For each of the following events, consider how you might react. What things might you consume more or less of? Would you work more or less? Would you increase or decrease your saving?
a. You have a very close friend who lives in another city, a 3-hour bus ride away. The price of a round-trip ticket rises from $20 to $45.
b

Consider a firm where production depends on two inputs: labor and capital, with prices w and r, respectively. Initially, the firm faces market prices of w=6 and r=4. these prices then shift to w=4 and r=2.
a) in which direction with the substitutioneffect change the firm's employment and capital stock?
b) in which directi

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Managers are very interested in how a consumer makes a choice among alternatives. In this exercise, we ask you to consider the amount of money you spend purchasing gasoline to operate your automobile for a month and any alternatives available to you assuming your net income available to make those purchases. Also assume gasoline

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a. people drove less and purchased less gas
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c. people had mo

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Please help me with this question.

Find the integral using each method.
Integral x * sq. rt 4 + x dx
a) trigonometric substitution
b) Substitution: u^2 = 4 + x
c) Substitution: u = 4 + x
d) Integration by parts: dv = sq. rt. 4 + x dx
Thanks.

In the context of usual utility maximization problems involving two goods, prove that:
a) All goods must have one net substitute.
b) An inferior good must have at least one gross substitute.