Utility Maximization: Perfect Complements

If we always consume alpha units of good 1 with 1 unit of good 2 (say, 2 spoons of sugar with one cup of coffee), then given the budget, what is the optimal of good 1 and good 2 purchased?

[ulvumustafayev]

Hi.Thank you for this excellent presentation.I have watched all the videos and find them super useful.Unfortunately, there 2 exercises about game theory that I can't solve.Pleaseee could you help me? Pleasee
This is the exercise:

 A). Consider a duopoly with differentiated products. The two firms are denoted 1 and 2, and their
products q1 and q2 with prices p1 and p2, respectively. There is a representative consumer whose net
utility from purchasing the two goods is U=q1+q2-1/2(q1 ^2 + q2^2)-yq1q2-p1q1-p2q2

The parameter y, which ranges in between 0 and 1, is the degree of product differentiation (products
are perfect substitutes when y= 1, while they are independent when y= 0. Firms have symmetric
and constant marginal cost c  1.
1. Derive the direct and indirect demand functions (i.e., quantities as function of prices, and prices as
function of quantities)
2. Consider then the case of quantity competition (Cournot). Derive the best response functions and
the Nash equilibrium, as a function of the parameters y and c.
3. Do the same for the case of price competition (Bertrand).
4. Compare the two equilibria. Which one is preferred by the firms? And by the consumer?

B.  Consider a sealed‐bid first‐price auction. There are two bidders, 1 and 2, with valuations for the good
of v1 and v2, respectively. Each buyer’s valuation is his/her own private information. v1 is uniformly
distributed on include (0, 1) and v2 is uniformly distributed on include (0, 2). So player 1, for instance, knows  v1 exactly
but regarding v2 he/she knows only that it is uniformly distributed between 0 and 2. 
1. Define the Bayesian equilibrium for this game.
2. Find a Bayesian equilibrium. 
3. Discuss uniqueness.

[abdulrazack]

in my text book there's nothing like an alpha, so i don't know I kind of got lost with the alpha thing. Was it alpha, or maybe am even saying it wrong.

[mogoggy]

Why is utility 12 isn't that just the quantity?

[Raskolnikovishere]

Thankyou so much for this video, I was super stuck in the weeds of derivatives but you cleared it all up :)