Imagine a society that produces military goods and consumer goods, which we’ll call “guns” and “butter.” a. Draw a production possibilities frontier for guns and butter. Using the concept of opportunity cost, explain why it most likely has a bowed-out shape. b. Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient. c. Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point that the Doves might choose. d. Imagine that an aggressive neighboring country reduces the size of its military. As a result, both the Hawks and the Doves reduce their desired production of guns by the same amount. Which party would get the bigger “peace dividend,” measured by the increase in butter production? Explain.

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."

Imagine that an aggressive neighboring country reduces the size of its military. As a result, both the Hawks and the Doves reduce their desired production of guns by the same amount. Which party would get the bigger "peace dividend," measured by the increase in butter production? Explain.

An economy consists of three workers: Larry, Moe, and Curly. Each works 10 hours a day and can produce two services: mowing lawns and washing cars. In an hour Larry can either mow one lawn or wash one car; Moe can either mow one lawn or wash two cars; and Curly can either mow two lawns or wash one car. a. Calculate how much of each service is produced under the following circumstances, which we label A, B, C, and D: • All three spend all their time mowing lawns. (A) • All three spend all their time washing cars. (B) • All three spend half their time on each activity. (C) • Larry spends half his time on each activity, while Moe only washes cars and Curly only mows lawns. (D) b. Graph the production possibilities frontier for this economy. Using your answers to part (a), identify points A, B, C, and D on your graph. c. Explain why the production possibilities frontier has the shape it does. d. Are any of the allocations calculated in part (a) inefficient? Explain.

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."

Draw a production possibilities frontier for guns and butter. Using the concept of opportunity cost, explain why it most likely has a bowed-out shape.

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."

Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point that the Doves might choose.

Imagine a society that produces military goods and consumer goods, which we'll call "guns" and "butter."

Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point that the Doves might choose.

State the amplitude, where appropriate, of: y = sin 4x

(a) Let $f :\mathbb{R}^3 \to \mathbb{R}, \mathbf{x}_0 \in \mathbb{R}^3$. If $\mathbf{v}$ is a unit vector in $\mathbb{R}^3$, show that the maximum value of the directional derivative of $f$ at $\mathbf{x}_0$ along $\mathbf{v}$ is $||\nabla f (\mathbf{x}_0)||$.

suppose $y = f (x)$ is defined for all $x$. For each description, sketch a graph with the indicated property.

Discontinuous at $x=2$ but continuous elsewhere with $\lim _{x \rightarrow 0} f(x)=\frac{1}{2}$

Zinc reacts with 100.0 mL of 6.00 M cold, aqueous sulfuric acid through single replacement. a. How many grams of zinc sulfate can be produced? b. How many liters of hydrogen gas could be released at STP?

Write the rule for a quadratic function with a vertex of (0,0) that passes through (-1,3).

"Imagine a society that produces military goods and consumer goods, which we’ll call “guns” and “butter.”

Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient."

Suggest an explanation for why aspirin has a sour taste.

a. For what values of a and b will

$$g(x)=\left\{\begin{array}{ll}{a x+b,} & {x \leq-1} \\ {a x^{3}+x+2 b,} & {x>-1}\end{array}\right.$$

be differentiable for all values of x? b. Discuss the geometry of the resulting graph of g.